时序数据的因果效应推断#
在本 Notebook 中，我们将探讨一个从时序数据推断因果效应的示例。我们将使用 DoWhy 的功能向因果图添加时间依赖关系，并基于增强图估计因果效应。
[1]:
import networkx as nx
import pandas as pd
from dowhy.utils.timeseries import create_graph_from_csv,create_graph_from_user
from dowhy.utils.plotting import plot, pretty_print_graph
加载时序数据和因果图#
[2]:
dataset_path="../datasets/temporal_dataset.csv"
dataframe=pd.read_csv(dataset_path)
在时序因果推断中，准确估计因果效应通常需要考虑图中节点之间的时间滞后。例如，如果 \(node_1\) 对 \(node_2\) 的影响存在 5 个时间戳的时间滞后，我们将这种依赖关系表示为 \(node_1^{t-5}\) -> \(node_2^{t}\)。
我们可以将因果图作为 networkx DAG 或 dot 文件提供。边属性应提及与每条边关联的确切 time_lag（如果有）。
[3]:
from dowhy.utils.timeseries import create_graph_from_dot_format
file_path = "../datasets/temporal_graph.dot"
graph = create_graph_from_dot_format(file_path)
plot(graph)
我们还可以创建一个 CSV 文件，其中包含时序图中的边。CSV 中的列为 node1、node2、time_lag，表示一条有向边 node1 -> node2，时间滞后为 time_lag。让我们考虑以下图作为输入
节点1 |
节点2 |
时间滞后 |
|---|---|---|
V1 |
V2 |
3 |
V2 |
V3 |
4 |
V5 |
V6 |
1 |
V4 |
V7 |
4 |
V4 |
V5 |
2 |
V7 |
V6 |
3 |
V7 |
V6 |
5 |
[4]:
# Input a csv file with the edges in the graph with the columns: node_1,node_2,time_lag
file_path = "../datasets/temporal_graph.csv"
# Create the graph from the CSV file
graph = create_graph_from_csv(file_path)
plot(graph)
数据集偏移和过滤#
为了准备用于时序因果推断的数据集，我们需要根据给定的时间滞后对列进行偏移。
例如，在上面的因果图中，\(node_1^{t-5}\) -> \(node_2^{t}\) 的滞后为 5。当将 \(node_2\) 视为目标节点时，\(node_1\) 的数据应向下偏移 5 个时间戳。这种调整确保了边 \(node_1\) -> \(node_2\) 准确地表示了滞后依赖关系。以这种方式偏移数据会创建额外的列，并允许下游估计器访问 DataFrame 同一行中的正确值。
[5]:
from dowhy.timeseries.temporal_shift import shift_columns_by_lag_using_unrolled_graph, add_lagged_edges
[6]:
# the outcome node for which effect estimation has to be done, node:6
target_node = 'V6'
unrolled_graph = add_lagged_edges(graph, target_node)
plot(unrolled_graph)
[7]:
time_shifted_df = shift_columns_by_lag_using_unrolled_graph(dataframe, unrolled_graph)
time_shifted_df.head()
[7]:
| V6_0 | V5_-1 | V7_-3 | V7_-5 | V4_-3 | V4_-7 | V4_-9 | |
|---|---|---|---|---|---|---|---|
| 0 | 6 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 7 | 5 | 0 | 0 | 0 | 0 | 0 |
| 2 | 8 | 6 | 0 | 0 | 0 | 0 | 0 |
| 3 | 9 | 7 | 7 | 0 | 4 | 0 | 0 |
| 4 | 9 | 8 | 8 | 0 | 5 | 0 | 0 |
因果效应估计#
有了新的 DataFrame 后，就可以对目标节点相对于行动节点进行因果效应估计。
[8]:
target_node = 'V6_0'
# include all the treatments
treatment_columns = list(time_shifted_df.columns)
treatment_columns.remove(target_node)
treatment_columns
[8]:
['V5_-1', 'V7_-3', 'V7_-5', 'V4_-3', 'V4_-7', 'V4_-9']
[9]:
# perform causal effect estimation on this new dataset
import dowhy
from dowhy import CausalModel
model = CausalModel(
data=time_shifted_df,
treatment='V5_-1',
outcome=target_node,
graph = unrolled_graph
)
identified_estimand = model.identify_effect()
estimate = model.estimate_effect(identified_estimand,
method_name="backdoor.linear_regression",
test_significance=True)
print(estimate)
*** Causal Estimate ***
## Identified estimand
Estimand type: EstimandType.NONPARAMETRIC_ATE
### Estimand : 1
Estimand name: backdoor
Estimand expression:
d
────────(E[V_6_0|V4_-7])
d[V₅ ₋₁]
Estimand assumption 1, Unconfoundedness: If U→{V5_-1} and U→V6_0 then P(V6_0|V5_-1,V4_-7,U) = P(V6_0|V5_-1,V4_-7)
## Realized estimand
b: V6_0~V5_-1+V4_-7+V5_-1*V7_-3+V5_-1*V7_-5
Target units:
## Estimate
Mean value: -0.12612138021763197
p-value: [0.75401158]
### Conditional Estimates
__categorical__V7_-3 __categorical__V7_-5
(-0.001, 0.6] (-0.001, 5.4] 0.111915
(0.6, 5.4] (7.8, 9.0] -0.257861
(9.0, 10.0] -0.314176
(5.4, 7.8] (-0.001, 5.4] 0.073537
(7.8, 9.0] -0.285273
(7.8, 9.0] (-0.001, 5.4] -0.034356
(5.4, 7.8] -0.216503
(7.8, 9.0] -0.296238
(9.0, 10.0] (7.8, 9.0] -0.261853
dtype: float64
/github/home/.cache/pypoetry/virtualenvs/dowhy-oN2hW5jr-py3.8/lib/python3.8/site-packages/scipy/stats/_stats_py.py:1736: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=14
warnings.warn("kurtosistest only valid for n>=20 ... continuing "
从 Tigramite 库导入时序因果图#
Tigramite 是一个流行的时序因果发现库。本节重点介绍如何通过应用 Tigramite 中的 PCMCI+ 算法获取因果图并将其导入到 DoWhy 中。
[10]:
!pip install tigramite
Collecting tigramite
Downloading tigramite-5.2.6.5-py3-none-any.whl (300 kB)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 300.0/300.0 kB 15.3 MB/s eta 0:00:00
Requirement already satisfied: numpy>=1.18 in /github/home/.cache/pypoetry/virtualenvs/dowhy-oN2hW5jr-py3.8/lib/python3.8/site-packages (from tigramite) (1.24.4)
Requirement already satisfied: scipy>=1.10.0 in /github/home/.cache/pypoetry/virtualenvs/dowhy-oN2hW5jr-py3.8/lib/python3.8/site-packages (from tigramite) (1.10.1)
Requirement already satisfied: six in /github/home/.cache/pypoetry/virtualenvs/dowhy-oN2hW5jr-py3.8/lib/python3.8/site-packages (from tigramite) (1.16.0)
Installing collected packages: tigramite
Successfully installed tigramite-5.2.6.5
[notice] A new release of pip is available: 23.1.2 -> 24.3.1
[notice] To update, run: pip install --upgrade pip
[11]:
import tigramite
import tigramite.data_processing as pp
import matplotlib.pyplot as plt
import pandas as pd
dataframe = dataframe.astype(float)
var_names = dataframe.columns
# convert the dataframe values to float
dataframe = pp.DataFrame(dataframe.values, var_names=var_names)
[12]:
from tigramite import plotting as tp
tp.plot_timeseries(dataframe, figsize=(15, 5)); plt.show()
[13]:
from tigramite.pcmci import PCMCI
from tigramite.independence_tests.parcorr import ParCorr
import numpy as np
parcorr = ParCorr(significance='analytic')
pcmci = PCMCI(
dataframe=dataframe,
cond_ind_test=parcorr,
verbosity=1)
[14]:
correlations = pcmci.run_bivci(tau_max=3, val_only=True)['val_matrix']
matrix_lags = np.argmax(np.abs(correlations), axis=2)
##
## Running Tigramite BivCI algorithm
##
Parameters:
independence test = par_corr
tau_min = 0
tau_max = 3
[15]:
tau_max = 3
pc_alpha = None
pcmci.verbosity = 2
results = pcmci.run_pcmciplus(tau_min=0, tau_max=tau_max, pc_alpha=pc_alpha)
##
## Optimizing pc_alpha over pc_alpha_list = [0.001, 0.005, 0.01, 0.025, 0.05]
##
## pc_alpha = 0.001 (1/5):
##
## Step 1: PC1 algorithm for selecting lagged conditions
##
Parameters:
independence test = par_corr
tau_min = 1
tau_max = 3
pc_alpha = [0.001]
max_conds_dim = None
max_combinations = 1
## Variable V1
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V1 (1/21):
Subset 0: () gives pval = 0.86601 / val = -0.072
Non-significance detected.
Link (V1 -2) -?> V1 (2/21):
Subset 0: () gives pval = 0.57469 / val = -0.235
Non-significance detected.
Link (V1 -3) -?> V1 (3/21):
Subset 0: () gives pval = 0.13528 / val = -0.576
Non-significance detected.
Link (V2 -1) -?> V1 (4/21):
Subset 0: () gives pval = 0.08631 / val = 0.642
Non-significance detected.
Link (V2 -2) -?> V1 (5/21):
Subset 0: () gives pval = 1.00000 / val = -0.000
Non-significance detected.
Link (V2 -3) -?> V1 (6/21):
Subset 0: () gives pval = 0.08260 / val = -0.647
Non-significance detected.
Link (V3 -1) -?> V1 (7/21):
Subset 0: () gives pval = 0.30492 / val = -0.416
Non-significance detected.
Link (V3 -2) -?> V1 (8/21):
Subset 0: () gives pval = 0.90322 / val = -0.052
Non-significance detected.
Link (V3 -3) -?> V1 (9/21):
Subset 0: () gives pval = 0.59372 / val = 0.224
Non-significance detected.
Link (V4 -1) -?> V1 (10/21):
Subset 0: () gives pval = 0.08508 / val = -0.644
Non-significance detected.
Link (V4 -2) -?> V1 (11/21):
Subset 0: () gives pval = 0.21081 / val = -0.496
Non-significance detected.
Link (V4 -3) -?> V1 (12/21):
Subset 0: () gives pval = 0.26642 / val = 0.447
Non-significance detected.
Link (V5 -1) -?> V1 (13/21):
Subset 0: () gives pval = 0.36475 / val = -0.372
Non-significance detected.
Link (V5 -2) -?> V1 (14/21):
Subset 0: () gives pval = 0.97472 / val = -0.013
Non-significance detected.
Link (V5 -3) -?> V1 (15/21):
Subset 0: () gives pval = 0.28630 / val = 0.431
Non-significance detected.
Link (V6 -1) -?> V1 (16/21):
Subset 0: () gives pval = 0.69615 / val = -0.165
Non-significance detected.
Link (V6 -2) -?> V1 (17/21):
Subset 0: () gives pval = 0.60470 / val = 0.218
Non-significance detected.
Link (V6 -3) -?> V1 (18/21):
Subset 0: () gives pval = 0.64103 / val = 0.196
Non-significance detected.
Link (V7 -1) -?> V1 (19/21):
Subset 0: () gives pval = 0.32015 / val = 0.405
Non-significance detected.
Link (V7 -2) -?> V1 (20/21):
Subset 0: () gives pval = 0.67332 / val = -0.178
Non-significance detected.
Link (V7 -3) -?> V1 (21/21):
Subset 0: () gives pval = 0.52668 / val = 0.265
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V1 has 0 link(s):
Algorithm converged for variable V1
## Variable V2
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V2 (1/21):
Subset 0: () gives pval = 0.12317 / val = -0.591
Non-significance detected.
Link (V1 -2) -?> V2 (2/21):
Subset 0: () gives pval = 0.87304 / val = 0.068
Non-significance detected.
Link (V1 -3) -?> V2 (3/21):
Subset 0: () gives pval = 0.40658 / val = 0.342
Non-significance detected.
Link (V2 -1) -?> V2 (4/21):
Subset 0: () gives pval = 0.87285 / val = -0.068
Non-significance detected.
Link (V2 -2) -?> V2 (5/21):
Subset 0: () gives pval = 0.00058 / val = -0.938
No conditions of dimension 0 left.
Link (V2 -3) -?> V2 (6/21):
Subset 0: () gives pval = 0.38647 / val = 0.356
Non-significance detected.
Link (V3 -1) -?> V2 (7/21):
Subset 0: () gives pval = 0.18843 / val = -0.518
Non-significance detected.
Link (V3 -2) -?> V2 (8/21):
Subset 0: () gives pval = 0.82124 / val = 0.096
Non-significance detected.
Link (V3 -3) -?> V2 (9/21):
Subset 0: () gives pval = 0.25844 / val = 0.454
Non-significance detected.
Link (V4 -1) -?> V2 (10/21):
Subset 0: () gives pval = 0.08165 / val = -0.649
Non-significance detected.
Link (V4 -2) -?> V2 (11/21):
Subset 0: () gives pval = 0.06607 / val = 0.675
Non-significance detected.
Link (V4 -3) -?> V2 (12/21):
Subset 0: () gives pval = 0.58825 / val = 0.227
Non-significance detected.
Link (V5 -1) -?> V2 (13/21):
Subset 0: () gives pval = 0.38186 / val = -0.359
Non-significance detected.
Link (V5 -2) -?> V2 (14/21):
Subset 0: () gives pval = 0.32916 / val = 0.398
Non-significance detected.
Link (V5 -3) -?> V2 (15/21):
Subset 0: () gives pval = 0.98847 / val = 0.006
Non-significance detected.
Link (V6 -1) -?> V2 (16/21):
Subset 0: () gives pval = 0.32076 / val = 0.404
Non-significance detected.
Link (V6 -2) -?> V2 (17/21):
Subset 0: () gives pval = 0.40538 / val = 0.343
Non-significance detected.
Link (V6 -3) -?> V2 (18/21):
Subset 0: () gives pval = 0.37909 / val = -0.361
Non-significance detected.
Link (V7 -1) -?> V2 (19/21):
Subset 0: () gives pval = 0.96874 / val = -0.017
Non-significance detected.
Link (V7 -2) -?> V2 (20/21):
Subset 0: () gives pval = 0.29908 / val = 0.421
Non-significance detected.
Link (V7 -3) -?> V2 (21/21):
Subset 0: () gives pval = 0.32576 / val = 0.400
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Algorithm converged for variable V2
## Variable V3
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V3 (1/21):
Subset 0: () gives pval = 0.39391 / val = -0.351
Non-significance detected.
Link (V1 -2) -?> V3 (2/21):
Subset 0: () gives pval = 0.75698 / val = -0.131
Non-significance detected.
Link (V1 -3) -?> V3 (3/21):
Subset 0: () gives pval = 0.17237 / val = 0.534
Non-significance detected.
Link (V2 -1) -?> V3 (4/21):
Subset 0: () gives pval = 0.25198 / val = 0.460
Non-significance detected.
Link (V2 -2) -?> V3 (5/21):
Subset 0: () gives pval = 0.81987 / val = -0.097
Non-significance detected.
Link (V2 -3) -?> V3 (6/21):
Subset 0: () gives pval = 0.14919 / val = -0.560
Non-significance detected.
Link (V3 -1) -?> V3 (7/21):
Subset 0: () gives pval = 0.92814 / val = 0.038
Non-significance detected.
Link (V3 -2) -?> V3 (8/21):
Subset 0: () gives pval = 0.55198 / val = -0.249
Non-significance detected.
Link (V3 -3) -?> V3 (9/21):
Subset 0: () gives pval = 0.87647 / val = -0.066
Non-significance detected.
Link (V4 -1) -?> V3 (10/21):
Subset 0: () gives pval = 0.83660 / val = 0.088
Non-significance detected.
Link (V4 -2) -?> V3 (11/21):
Subset 0: () gives pval = 0.92891 / val = 0.038
Non-significance detected.
Link (V4 -3) -?> V3 (12/21):
Subset 0: () gives pval = 0.18176 / val = 0.525
Non-significance detected.
Link (V5 -1) -?> V3 (13/21):
Subset 0: () gives pval = 0.32210 / val = 0.403
Non-significance detected.
Link (V5 -2) -?> V3 (14/21):
Subset 0: () gives pval = 0.67508 / val = -0.177
Non-significance detected.
Link (V5 -3) -?> V3 (15/21):
Subset 0: () gives pval = 0.65106 / val = -0.191
Non-significance detected.
Link (V6 -1) -?> V3 (16/21):
Subset 0: () gives pval = 0.87265 / val = -0.068
Non-significance detected.
Link (V6 -2) -?> V3 (17/21):
Subset 0: () gives pval = 0.73304 / val = 0.144
Non-significance detected.
Link (V6 -3) -?> V3 (18/21):
Subset 0: () gives pval = 0.71062 / val = 0.157
Non-significance detected.
Link (V7 -1) -?> V3 (19/21):
Subset 0: () gives pval = 0.08132 / val = -0.650
Non-significance detected.
Link (V7 -2) -?> V3 (20/21):
Subset 0: () gives pval = 0.65185 / val = -0.190
Non-significance detected.
Link (V7 -3) -?> V3 (21/21):
Subset 0: () gives pval = 0.71587 / val = 0.154
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V3 has 0 link(s):
Algorithm converged for variable V3
## Variable V4
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V4 (1/21):
Subset 0: () gives pval = 0.56354 / val = 0.242
Non-significance detected.
Link (V1 -2) -?> V4 (2/21):
Subset 0: () gives pval = 0.58558 / val = 0.229
Non-significance detected.
Link (V1 -3) -?> V4 (3/21):
Subset 0: () gives pval = 0.96166 / val = -0.020
Non-significance detected.
Link (V2 -1) -?> V4 (4/21):
Subset 0: () gives pval = 0.16299 / val = 0.544
Non-significance detected.
Link (V2 -2) -?> V4 (5/21):
Subset 0: () gives pval = 0.24064 / val = 0.469
Non-significance detected.
Link (V2 -3) -?> V4 (6/21):
Subset 0: () gives pval = 0.06141 / val = -0.684
Non-significance detected.
Link (V3 -1) -?> V4 (7/21):
Subset 0: () gives pval = 0.94919 / val = 0.027
Non-significance detected.
Link (V3 -2) -?> V4 (8/21):
Subset 0: () gives pval = 0.02698 / val = -0.765
Non-significance detected.
Link (V3 -3) -?> V4 (9/21):
Subset 0: () gives pval = 0.35707 / val = -0.377
Non-significance detected.
Link (V4 -1) -?> V4 (10/21):
Subset 0: () gives pval = 0.77024 / val = 0.124
Non-significance detected.
Link (V4 -2) -?> V4 (11/21):
Subset 0: () gives pval = 0.12671 / val = -0.586
Non-significance detected.
Link (V4 -3) -?> V4 (12/21):
Subset 0: () gives pval = 0.87499 / val = -0.067
Non-significance detected.
Link (V5 -1) -?> V4 (13/21):
Subset 0: () gives pval = 0.45958 / val = -0.307
Non-significance detected.
Link (V5 -2) -?> V4 (14/21):
Subset 0: () gives pval = 0.72738 / val = -0.148
Non-significance detected.
Link (V5 -3) -?> V4 (15/21):
Subset 0: () gives pval = 0.29395 / val = -0.425
Non-significance detected.
Link (V6 -1) -?> V4 (16/21):
Subset 0: () gives pval = 0.88424 / val = 0.062
Non-significance detected.
Link (V6 -2) -?> V4 (17/21):
Subset 0: () gives pval = 0.17711 / val = 0.530
Non-significance detected.
Link (V6 -3) -?> V4 (18/21):
Subset 0: () gives pval = 0.81886 / val = 0.097
Non-significance detected.
Link (V7 -1) -?> V4 (19/21):
Subset 0: () gives pval = 0.80817 / val = 0.103
Non-significance detected.
Link (V7 -2) -?> V4 (20/21):
Subset 0: () gives pval = 0.93921 / val = 0.032
Non-significance detected.
Link (V7 -3) -?> V4 (21/21):
Subset 0: () gives pval = 0.21585 / val = 0.492
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V4 has 0 link(s):
Algorithm converged for variable V4
## Variable V5
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V5 (1/21):
Subset 0: () gives pval = 0.37886 / val = -0.362
Non-significance detected.
Link (V1 -2) -?> V5 (2/21):
Subset 0: () gives pval = 0.30644 / val = 0.415
Non-significance detected.
Link (V1 -3) -?> V5 (3/21):
Subset 0: () gives pval = 0.73999 / val = -0.141
Non-significance detected.
Link (V2 -1) -?> V5 (4/21):
Subset 0: () gives pval = 0.95989 / val = -0.021
Non-significance detected.
Link (V2 -2) -?> V5 (5/21):
Subset 0: () gives pval = 0.72633 / val = 0.148
Non-significance detected.
Link (V2 -3) -?> V5 (6/21):
Subset 0: () gives pval = 0.80597 / val = -0.104
Non-significance detected.
Link (V3 -1) -?> V5 (7/21):
Subset 0: () gives pval = 0.42170 / val = 0.332
Non-significance detected.
Link (V3 -2) -?> V5 (8/21):
Subset 0: () gives pval = 0.70342 / val = -0.161
Non-significance detected.
Link (V3 -3) -?> V5 (9/21):
Subset 0: () gives pval = 0.16043 / val = -0.547
Non-significance detected.
Link (V4 -1) -?> V5 (10/21):
Subset 0: () gives pval = 0.85612 / val = 0.077
Non-significance detected.
Link (V4 -2) -?> V5 (11/21):
Subset 0: () gives pval = 0.71488 / val = 0.155
Non-significance detected.
Link (V4 -3) -?> V5 (12/21):
Subset 0: () gives pval = 0.74776 / val = -0.136
Non-significance detected.
Link (V5 -1) -?> V5 (13/21):
Subset 0: () gives pval = 0.12982 / val = -0.582
Non-significance detected.
Link (V5 -2) -?> V5 (14/21):
Subset 0: () gives pval = 0.36498 / val = 0.371
Non-significance detected.
Link (V5 -3) -?> V5 (15/21):
Subset 0: () gives pval = 0.40910 / val = -0.341
Non-significance detected.
Link (V6 -1) -?> V5 (16/21):
Subset 0: () gives pval = 0.38906 / val = -0.354
Non-significance detected.
Link (V6 -2) -?> V5 (17/21):
Subset 0: () gives pval = 0.12547 / val = 0.588
Non-significance detected.
Link (V6 -3) -?> V5 (18/21):
Subset 0: () gives pval = 0.73154 / val = -0.145
Non-significance detected.
Link (V7 -1) -?> V5 (19/21):
Subset 0: () gives pval = 0.94756 / val = 0.028
Non-significance detected.
Link (V7 -2) -?> V5 (20/21):
Subset 0: () gives pval = 0.47394 / val = -0.298
Non-significance detected.
Link (V7 -3) -?> V5 (21/21):
Subset 0: () gives pval = 0.19310 / val = 0.513
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V5 has 0 link(s):
Algorithm converged for variable V5
## Variable V6
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V6 (1/21):
Subset 0: () gives pval = 0.38954 / val = 0.354
Non-significance detected.
Link (V1 -2) -?> V6 (2/21):
Subset 0: () gives pval = 0.13823 / val = 0.572
Non-significance detected.
Link (V1 -3) -?> V6 (3/21):
Subset 0: () gives pval = 0.13173 / val = -0.580
Non-significance detected.
Link (V2 -1) -?> V6 (4/21):
Subset 0: () gives pval = 0.45705 / val = -0.309
Non-significance detected.
Link (V2 -2) -?> V6 (5/21):
Subset 0: () gives pval = 0.59135 / val = 0.225
Non-significance detected.
Link (V2 -3) -?> V6 (6/21):
Subset 0: () gives pval = 0.46932 / val = 0.301
Non-significance detected.
Link (V3 -1) -?> V6 (7/21):
Subset 0: () gives pval = 0.19069 / val = -0.516
Non-significance detected.
Link (V3 -2) -?> V6 (8/21):
Subset 0: () gives pval = 0.81980 / val = 0.097
Non-significance detected.
Link (V3 -3) -?> V6 (9/21):
Subset 0: () gives pval = 0.92754 / val = -0.039
Non-significance detected.
Link (V4 -1) -?> V6 (10/21):
Subset 0: () gives pval = 0.79337 / val = -0.111
Non-significance detected.
Link (V4 -2) -?> V6 (11/21):
Subset 0: () gives pval = 0.42452 / val = -0.330
Non-significance detected.
Link (V4 -3) -?> V6 (12/21):
Subset 0: () gives pval = 0.11568 / val = -0.600
Non-significance detected.
Link (V5 -1) -?> V6 (13/21):
Subset 0: () gives pval = 0.26711 / val = -0.447
Non-significance detected.
Link (V5 -2) -?> V6 (14/21):
Subset 0: () gives pval = 0.73415 / val = -0.144
Non-significance detected.
Link (V5 -3) -?> V6 (15/21):
Subset 0: () gives pval = 0.89556 / val = 0.056
Non-significance detected.
Link (V6 -1) -?> V6 (16/21):
Subset 0: () gives pval = 0.59685 / val = 0.222
Non-significance detected.
Link (V6 -2) -?> V6 (17/21):
Subset 0: () gives pval = 0.75751 / val = -0.131
Non-significance detected.
Link (V6 -3) -?> V6 (18/21):
Subset 0: () gives pval = 0.41015 / val = -0.340
Non-significance detected.
Link (V7 -1) -?> V6 (19/21):
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Link (V7 -2) -?> V6 (20/21):
Subset 0: () gives pval = 0.48406 / val = 0.291
Non-significance detected.
Link (V7 -3) -?> V6 (21/21):
Subset 0: () gives pval = 0.81090 / val = -0.102
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Algorithm converged for variable V6
## Variable V7
Iterating through pc_alpha = [0.001]:
# pc_alpha = 0.001 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V7 (1/21):
Subset 0: () gives pval = 0.10602 / val = 0.613
Non-significance detected.
Link (V1 -2) -?> V7 (2/21):
Subset 0: () gives pval = 0.13143 / val = -0.580
Non-significance detected.
Link (V1 -3) -?> V7 (3/21):
Subset 0: () gives pval = 0.20399 / val = -0.503
Non-significance detected.
Link (V2 -1) -?> V7 (4/21):
Subset 0: () gives pval = 0.31711 / val = 0.407
Non-significance detected.
Link (V2 -2) -?> V7 (5/21):
Subset 0: () gives pval = 0.40496 / val = 0.343
Non-significance detected.
Link (V2 -3) -?> V7 (6/21):
Subset 0: () gives pval = 0.49089 / val = -0.287
Non-significance detected.
Link (V3 -1) -?> V7 (7/21):
Subset 0: () gives pval = 0.92032 / val = 0.043
Non-significance detected.
Link (V3 -2) -?> V7 (8/21):
Subset 0: () gives pval = 0.79775 / val = -0.109
Non-significance detected.
Link (V3 -3) -?> V7 (9/21):
Subset 0: () gives pval = 0.75377 / val = 0.133
Non-significance detected.
Link (V4 -1) -?> V7 (10/21):
Subset 0: () gives pval = 0.75703 / val = -0.131
Non-significance detected.
Link (V4 -2) -?> V7 (11/21):
Subset 0: () gives pval = 0.07150 / val = -0.666
Non-significance detected.
Link (V4 -3) -?> V7 (12/21):
Subset 0: () gives pval = 0.87683 / val = 0.066
Non-significance detected.
Link (V5 -1) -?> V7 (13/21):
Subset 0: () gives pval = 0.97094 / val = 0.016
Non-significance detected.
Link (V5 -2) -?> V7 (14/21):
Subset 0: () gives pval = 0.62396 / val = -0.206
Non-significance detected.
Link (V5 -3) -?> V7 (15/21):
Subset 0: () gives pval = 0.16865 / val = 0.538
Non-significance detected.
Link (V6 -1) -?> V7 (16/21):
Subset 0: () gives pval = 0.98554 / val = -0.008
Non-significance detected.
Link (V6 -2) -?> V7 (17/21):
Subset 0: () gives pval = 0.90824 / val = -0.049
Non-significance detected.
Link (V6 -3) -?> V7 (18/21):
Subset 0: () gives pval = 0.13870 / val = 0.572
Non-significance detected.
Link (V7 -1) -?> V7 (19/21):
Subset 0: () gives pval = 0.50733 / val = 0.277
Non-significance detected.
Link (V7 -2) -?> V7 (20/21):
Subset 0: () gives pval = 0.93834 / val = 0.033
Non-significance detected.
Link (V7 -3) -?> V7 (21/21):
Subset 0: () gives pval = 0.92994 / val = -0.037
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V7 has 0 link(s):
Algorithm converged for variable V7
## Resulting lagged parent (super)sets:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Variable V7 has 0 link(s):
##
## Step 2: PC algorithm with contemp. conditions and MCI tests
##
Parameters:
independence test = par_corr
tau_min = 0
tau_max = 3
pc_alpha = 0.001
contemp_collider_rule = majority
conflict_resolution = True
reset_lagged_links = False
max_conds_dim = None
max_conds_py = None
max_conds_px = None
max_conds_px_lagged = None
fdr_method = none
--------------------------
Skeleton discovery phase
--------------------------
Testing contemporaneous condition sets of dimension 0:
Link (V1 0) o?o V2 (1/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V2 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.78838 / val = 0.126
Non-significance detected.
Link (V1 0) o?o V3 (2/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.96748 / val = 0.017
Non-significance detected.
Link (V1 0) o?o V4 (3/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.39632 / val = 0.349
Non-significance detected.
Link (V1 0) o?o V5 (4/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.89723 / val = 0.055
Non-significance detected.
Link (V1 0) o?o V6 (5/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.46578 / val = -0.333
Non-significance detected.
Link (V1 0) o?o V7 (6/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32813 / val = 0.399
Non-significance detected.
Link (V2 0) o?o V1 (7/44):
Already removed.
Link (V2 -2) -?> V2 (8/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -4) ]
Subset 0: () gives pval = 0.00773 / val = -0.887
Non-significance detected.
Link (V2 0) o?o V3 (9/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.11874 / val = -0.644
Non-significance detected.
Link (V2 0) o?o V4 (10/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.64856 / val = 0.212
Non-significance detected.
Link (V2 0) o?o V5 (11/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.33073 / val = 0.434
Non-significance detected.
Link (V2 0) o?o V6 (12/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.49710 / val = 0.349
Non-significance detected.
Link (V2 0) o?o V7 (13/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.93791 / val = -0.037
Non-significance detected.
Link (V3 0) o?o V1 (14/44):
Already removed.
Link (V3 0) o?o V2 (15/44):
Already removed.
Link (V3 0) o?o V4 (16/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.30341 / val = 0.417
Non-significance detected.
Link (V3 0) o?o V5 (17/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.95447 / val = 0.024
Non-significance detected.
Link (V3 0) o?o V6 (18/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.53674 / val = -0.284
Non-significance detected.
Link (V3 0) o?o V7 (19/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.25153 / val = -0.460
Non-significance detected.
Link (V4 0) o?o V1 (20/44):
Already removed.
Link (V4 0) o?o V2 (21/44):
Already removed.
Link (V4 0) o?o V3 (22/44):
Already removed.
Link (V4 0) o?o V5 (23/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.20930 / val = 0.498
Non-significance detected.
Link (V4 0) o?o V6 (24/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.26768 / val = -0.487
Non-significance detected.
Link (V4 0) o?o V7 (25/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.92759 / val = -0.039
Non-significance detected.
Link (V5 0) o?o V1 (26/44):
Already removed.
Link (V5 0) o?o V2 (27/44):
Already removed.
Link (V5 0) o?o V3 (28/44):
Already removed.
Link (V5 0) o?o V4 (29/44):
Already removed.
Link (V5 0) o?o V6 (30/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.38468 / val = 0.392
Non-significance detected.
Link (V5 0) o?o V7 (31/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32066 / val = -0.404
Non-significance detected.
Link (V6 0) o?o V1 (32/44):
Already removed.
Link (V6 0) o?o V2 (33/44):
Already removed.
Link (V6 0) o?o V3 (34/44):
Already removed.
Link (V6 0) o?o V4 (35/44):
Already removed.
Link (V6 0) o?o V5 (36/44):
Already removed.
Link (V6 0) o?o V7 (37/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V7 -1) ]
Subset 0: () gives pval = 0.09642 / val = -0.675
Non-significance detected.
Link (V7 0) o?o V1 (38/44):
Already removed.
Link (V7 0) o?o V2 (39/44):
Already removed.
Link (V7 0) o?o V3 (40/44):
Already removed.
Link (V7 0) o?o V4 (41/44):
Already removed.
Link (V7 0) o?o V5 (42/44):
Already removed.
Link (V7 0) o?o V6 (43/44):
Already removed.
Link (V7 -1) -?> V6 (44/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Updated contemp. adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 0 link(s):
Variable V7 has 0 link(s):
Algorithm converged at p = 0.
----------------------------
Collider orientation phase
----------------------------
contemp_collider_rule = majority
conflict_resolution = True
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
----------------------------
Rule orientation phase
----------------------------
Try rule(s) [1 2 3]
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
## Significant links at alpha = 0.001:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): pval = 0.00000 | val = 0.992
Variable V7 has 0 link(s):
## pc_alpha = 0.005 (2/5):
##
## Step 1: PC1 algorithm for selecting lagged conditions
##
Parameters:
independence test = par_corr
tau_min = 1
tau_max = 3
pc_alpha = [0.005]
max_conds_dim = None
max_combinations = 1
## Variable V1
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V1 (1/21):
Subset 0: () gives pval = 0.86601 / val = -0.072
Non-significance detected.
Link (V1 -2) -?> V1 (2/21):
Subset 0: () gives pval = 0.57469 / val = -0.235
Non-significance detected.
Link (V1 -3) -?> V1 (3/21):
Subset 0: () gives pval = 0.13528 / val = -0.576
Non-significance detected.
Link (V2 -1) -?> V1 (4/21):
Subset 0: () gives pval = 0.08631 / val = 0.642
Non-significance detected.
Link (V2 -2) -?> V1 (5/21):
Subset 0: () gives pval = 1.00000 / val = -0.000
Non-significance detected.
Link (V2 -3) -?> V1 (6/21):
Subset 0: () gives pval = 0.08260 / val = -0.647
Non-significance detected.
Link (V3 -1) -?> V1 (7/21):
Subset 0: () gives pval = 0.30492 / val = -0.416
Non-significance detected.
Link (V3 -2) -?> V1 (8/21):
Subset 0: () gives pval = 0.90322 / val = -0.052
Non-significance detected.
Link (V3 -3) -?> V1 (9/21):
Subset 0: () gives pval = 0.59372 / val = 0.224
Non-significance detected.
Link (V4 -1) -?> V1 (10/21):
Subset 0: () gives pval = 0.08508 / val = -0.644
Non-significance detected.
Link (V4 -2) -?> V1 (11/21):
Subset 0: () gives pval = 0.21081 / val = -0.496
Non-significance detected.
Link (V4 -3) -?> V1 (12/21):
Subset 0: () gives pval = 0.26642 / val = 0.447
Non-significance detected.
Link (V5 -1) -?> V1 (13/21):
Subset 0: () gives pval = 0.36475 / val = -0.372
Non-significance detected.
Link (V5 -2) -?> V1 (14/21):
Subset 0: () gives pval = 0.97472 / val = -0.013
Non-significance detected.
Link (V5 -3) -?> V1 (15/21):
Subset 0: () gives pval = 0.28630 / val = 0.431
Non-significance detected.
Link (V6 -1) -?> V1 (16/21):
Subset 0: () gives pval = 0.69615 / val = -0.165
Non-significance detected.
Link (V6 -2) -?> V1 (17/21):
Subset 0: () gives pval = 0.60470 / val = 0.218
Non-significance detected.
Link (V6 -3) -?> V1 (18/21):
Subset 0: () gives pval = 0.64103 / val = 0.196
Non-significance detected.
Link (V7 -1) -?> V1 (19/21):
Subset 0: () gives pval = 0.32015 / val = 0.405
Non-significance detected.
Link (V7 -2) -?> V1 (20/21):
Subset 0: () gives pval = 0.67332 / val = -0.178
Non-significance detected.
Link (V7 -3) -?> V1 (21/21):
Subset 0: () gives pval = 0.52668 / val = 0.265
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V1 has 0 link(s):
Algorithm converged for variable V1
## Variable V2
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V2 (1/21):
Subset 0: () gives pval = 0.12317 / val = -0.591
Non-significance detected.
Link (V1 -2) -?> V2 (2/21):
Subset 0: () gives pval = 0.87304 / val = 0.068
Non-significance detected.
Link (V1 -3) -?> V2 (3/21):
Subset 0: () gives pval = 0.40658 / val = 0.342
Non-significance detected.
Link (V2 -1) -?> V2 (4/21):
Subset 0: () gives pval = 0.87285 / val = -0.068
Non-significance detected.
Link (V2 -2) -?> V2 (5/21):
Subset 0: () gives pval = 0.00058 / val = -0.938
No conditions of dimension 0 left.
Link (V2 -3) -?> V2 (6/21):
Subset 0: () gives pval = 0.38647 / val = 0.356
Non-significance detected.
Link (V3 -1) -?> V2 (7/21):
Subset 0: () gives pval = 0.18843 / val = -0.518
Non-significance detected.
Link (V3 -2) -?> V2 (8/21):
Subset 0: () gives pval = 0.82124 / val = 0.096
Non-significance detected.
Link (V3 -3) -?> V2 (9/21):
Subset 0: () gives pval = 0.25844 / val = 0.454
Non-significance detected.
Link (V4 -1) -?> V2 (10/21):
Subset 0: () gives pval = 0.08165 / val = -0.649
Non-significance detected.
Link (V4 -2) -?> V2 (11/21):
Subset 0: () gives pval = 0.06607 / val = 0.675
Non-significance detected.
Link (V4 -3) -?> V2 (12/21):
Subset 0: () gives pval = 0.58825 / val = 0.227
Non-significance detected.
Link (V5 -1) -?> V2 (13/21):
Subset 0: () gives pval = 0.38186 / val = -0.359
Non-significance detected.
Link (V5 -2) -?> V2 (14/21):
Subset 0: () gives pval = 0.32916 / val = 0.398
Non-significance detected.
Link (V5 -3) -?> V2 (15/21):
Subset 0: () gives pval = 0.98847 / val = 0.006
Non-significance detected.
Link (V6 -1) -?> V2 (16/21):
Subset 0: () gives pval = 0.32076 / val = 0.404
Non-significance detected.
Link (V6 -2) -?> V2 (17/21):
Subset 0: () gives pval = 0.40538 / val = 0.343
Non-significance detected.
Link (V6 -3) -?> V2 (18/21):
Subset 0: () gives pval = 0.37909 / val = -0.361
Non-significance detected.
Link (V7 -1) -?> V2 (19/21):
Subset 0: () gives pval = 0.96874 / val = -0.017
Non-significance detected.
Link (V7 -2) -?> V2 (20/21):
Subset 0: () gives pval = 0.29908 / val = 0.421
Non-significance detected.
Link (V7 -3) -?> V2 (21/21):
Subset 0: () gives pval = 0.32576 / val = 0.400
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Algorithm converged for variable V2
## Variable V3
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V3 (1/21):
Subset 0: () gives pval = 0.39391 / val = -0.351
Non-significance detected.
Link (V1 -2) -?> V3 (2/21):
Subset 0: () gives pval = 0.75698 / val = -0.131
Non-significance detected.
Link (V1 -3) -?> V3 (3/21):
Subset 0: () gives pval = 0.17237 / val = 0.534
Non-significance detected.
Link (V2 -1) -?> V3 (4/21):
Subset 0: () gives pval = 0.25198 / val = 0.460
Non-significance detected.
Link (V2 -2) -?> V3 (5/21):
Subset 0: () gives pval = 0.81987 / val = -0.097
Non-significance detected.
Link (V2 -3) -?> V3 (6/21):
Subset 0: () gives pval = 0.14919 / val = -0.560
Non-significance detected.
Link (V3 -1) -?> V3 (7/21):
Subset 0: () gives pval = 0.92814 / val = 0.038
Non-significance detected.
Link (V3 -2) -?> V3 (8/21):
Subset 0: () gives pval = 0.55198 / val = -0.249
Non-significance detected.
Link (V3 -3) -?> V3 (9/21):
Subset 0: () gives pval = 0.87647 / val = -0.066
Non-significance detected.
Link (V4 -1) -?> V3 (10/21):
Subset 0: () gives pval = 0.83660 / val = 0.088
Non-significance detected.
Link (V4 -2) -?> V3 (11/21):
Subset 0: () gives pval = 0.92891 / val = 0.038
Non-significance detected.
Link (V4 -3) -?> V3 (12/21):
Subset 0: () gives pval = 0.18176 / val = 0.525
Non-significance detected.
Link (V5 -1) -?> V3 (13/21):
Subset 0: () gives pval = 0.32210 / val = 0.403
Non-significance detected.
Link (V5 -2) -?> V3 (14/21):
Subset 0: () gives pval = 0.67508 / val = -0.177
Non-significance detected.
Link (V5 -3) -?> V3 (15/21):
Subset 0: () gives pval = 0.65106 / val = -0.191
Non-significance detected.
Link (V6 -1) -?> V3 (16/21):
Subset 0: () gives pval = 0.87265 / val = -0.068
Non-significance detected.
Link (V6 -2) -?> V3 (17/21):
Subset 0: () gives pval = 0.73304 / val = 0.144
Non-significance detected.
Link (V6 -3) -?> V3 (18/21):
Subset 0: () gives pval = 0.71062 / val = 0.157
Non-significance detected.
Link (V7 -1) -?> V3 (19/21):
Subset 0: () gives pval = 0.08132 / val = -0.650
Non-significance detected.
Link (V7 -2) -?> V3 (20/21):
Subset 0: () gives pval = 0.65185 / val = -0.190
Non-significance detected.
Link (V7 -3) -?> V3 (21/21):
Subset 0: () gives pval = 0.71587 / val = 0.154
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V3 has 0 link(s):
Algorithm converged for variable V3
## Variable V4
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V4 (1/21):
Subset 0: () gives pval = 0.56354 / val = 0.242
Non-significance detected.
Link (V1 -2) -?> V4 (2/21):
Subset 0: () gives pval = 0.58558 / val = 0.229
Non-significance detected.
Link (V1 -3) -?> V4 (3/21):
Subset 0: () gives pval = 0.96166 / val = -0.020
Non-significance detected.
Link (V2 -1) -?> V4 (4/21):
Subset 0: () gives pval = 0.16299 / val = 0.544
Non-significance detected.
Link (V2 -2) -?> V4 (5/21):
Subset 0: () gives pval = 0.24064 / val = 0.469
Non-significance detected.
Link (V2 -3) -?> V4 (6/21):
Subset 0: () gives pval = 0.06141 / val = -0.684
Non-significance detected.
Link (V3 -1) -?> V4 (7/21):
Subset 0: () gives pval = 0.94919 / val = 0.027
Non-significance detected.
Link (V3 -2) -?> V4 (8/21):
Subset 0: () gives pval = 0.02698 / val = -0.765
Non-significance detected.
Link (V3 -3) -?> V4 (9/21):
Subset 0: () gives pval = 0.35707 / val = -0.377
Non-significance detected.
Link (V4 -1) -?> V4 (10/21):
Subset 0: () gives pval = 0.77024 / val = 0.124
Non-significance detected.
Link (V4 -2) -?> V4 (11/21):
Subset 0: () gives pval = 0.12671 / val = -0.586
Non-significance detected.
Link (V4 -3) -?> V4 (12/21):
Subset 0: () gives pval = 0.87499 / val = -0.067
Non-significance detected.
Link (V5 -1) -?> V4 (13/21):
Subset 0: () gives pval = 0.45958 / val = -0.307
Non-significance detected.
Link (V5 -2) -?> V4 (14/21):
Subset 0: () gives pval = 0.72738 / val = -0.148
Non-significance detected.
Link (V5 -3) -?> V4 (15/21):
Subset 0: () gives pval = 0.29395 / val = -0.425
Non-significance detected.
Link (V6 -1) -?> V4 (16/21):
Subset 0: () gives pval = 0.88424 / val = 0.062
Non-significance detected.
Link (V6 -2) -?> V4 (17/21):
Subset 0: () gives pval = 0.17711 / val = 0.530
Non-significance detected.
Link (V6 -3) -?> V4 (18/21):
Subset 0: () gives pval = 0.81886 / val = 0.097
Non-significance detected.
Link (V7 -1) -?> V4 (19/21):
Subset 0: () gives pval = 0.80817 / val = 0.103
Non-significance detected.
Link (V7 -2) -?> V4 (20/21):
Subset 0: () gives pval = 0.93921 / val = 0.032
Non-significance detected.
Link (V7 -3) -?> V4 (21/21):
Subset 0: () gives pval = 0.21585 / val = 0.492
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V4 has 0 link(s):
Algorithm converged for variable V4
## Variable V5
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V5 (1/21):
Subset 0: () gives pval = 0.37886 / val = -0.362
Non-significance detected.
Link (V1 -2) -?> V5 (2/21):
Subset 0: () gives pval = 0.30644 / val = 0.415
Non-significance detected.
Link (V1 -3) -?> V5 (3/21):
Subset 0: () gives pval = 0.73999 / val = -0.141
Non-significance detected.
Link (V2 -1) -?> V5 (4/21):
Subset 0: () gives pval = 0.95989 / val = -0.021
Non-significance detected.
Link (V2 -2) -?> V5 (5/21):
Subset 0: () gives pval = 0.72633 / val = 0.148
Non-significance detected.
Link (V2 -3) -?> V5 (6/21):
Subset 0: () gives pval = 0.80597 / val = -0.104
Non-significance detected.
Link (V3 -1) -?> V5 (7/21):
Subset 0: () gives pval = 0.42170 / val = 0.332
Non-significance detected.
Link (V3 -2) -?> V5 (8/21):
Subset 0: () gives pval = 0.70342 / val = -0.161
Non-significance detected.
Link (V3 -3) -?> V5 (9/21):
Subset 0: () gives pval = 0.16043 / val = -0.547
Non-significance detected.
Link (V4 -1) -?> V5 (10/21):
Subset 0: () gives pval = 0.85612 / val = 0.077
Non-significance detected.
Link (V4 -2) -?> V5 (11/21):
Subset 0: () gives pval = 0.71488 / val = 0.155
Non-significance detected.
Link (V4 -3) -?> V5 (12/21):
Subset 0: () gives pval = 0.74776 / val = -0.136
Non-significance detected.
Link (V5 -1) -?> V5 (13/21):
Subset 0: () gives pval = 0.12982 / val = -0.582
Non-significance detected.
Link (V5 -2) -?> V5 (14/21):
Subset 0: () gives pval = 0.36498 / val = 0.371
Non-significance detected.
Link (V5 -3) -?> V5 (15/21):
Subset 0: () gives pval = 0.40910 / val = -0.341
Non-significance detected.
Link (V6 -1) -?> V5 (16/21):
Subset 0: () gives pval = 0.38906 / val = -0.354
Non-significance detected.
Link (V6 -2) -?> V5 (17/21):
Subset 0: () gives pval = 0.12547 / val = 0.588
Non-significance detected.
Link (V6 -3) -?> V5 (18/21):
Subset 0: () gives pval = 0.73154 / val = -0.145
Non-significance detected.
Link (V7 -1) -?> V5 (19/21):
Subset 0: () gives pval = 0.94756 / val = 0.028
Non-significance detected.
Link (V7 -2) -?> V5 (20/21):
Subset 0: () gives pval = 0.47394 / val = -0.298
Non-significance detected.
Link (V7 -3) -?> V5 (21/21):
Subset 0: () gives pval = 0.19310 / val = 0.513
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V5 has 0 link(s):
Algorithm converged for variable V5
## Variable V6
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V6 (1/21):
Subset 0: () gives pval = 0.38954 / val = 0.354
Non-significance detected.
Link (V1 -2) -?> V6 (2/21):
Subset 0: () gives pval = 0.13823 / val = 0.572
Non-significance detected.
Link (V1 -3) -?> V6 (3/21):
Subset 0: () gives pval = 0.13173 / val = -0.580
Non-significance detected.
Link (V2 -1) -?> V6 (4/21):
Subset 0: () gives pval = 0.45705 / val = -0.309
Non-significance detected.
Link (V2 -2) -?> V6 (5/21):
Subset 0: () gives pval = 0.59135 / val = 0.225
Non-significance detected.
Link (V2 -3) -?> V6 (6/21):
Subset 0: () gives pval = 0.46932 / val = 0.301
Non-significance detected.
Link (V3 -1) -?> V6 (7/21):
Subset 0: () gives pval = 0.19069 / val = -0.516
Non-significance detected.
Link (V3 -2) -?> V6 (8/21):
Subset 0: () gives pval = 0.81980 / val = 0.097
Non-significance detected.
Link (V3 -3) -?> V6 (9/21):
Subset 0: () gives pval = 0.92754 / val = -0.039
Non-significance detected.
Link (V4 -1) -?> V6 (10/21):
Subset 0: () gives pval = 0.79337 / val = -0.111
Non-significance detected.
Link (V4 -2) -?> V6 (11/21):
Subset 0: () gives pval = 0.42452 / val = -0.330
Non-significance detected.
Link (V4 -3) -?> V6 (12/21):
Subset 0: () gives pval = 0.11568 / val = -0.600
Non-significance detected.
Link (V5 -1) -?> V6 (13/21):
Subset 0: () gives pval = 0.26711 / val = -0.447
Non-significance detected.
Link (V5 -2) -?> V6 (14/21):
Subset 0: () gives pval = 0.73415 / val = -0.144
Non-significance detected.
Link (V5 -3) -?> V6 (15/21):
Subset 0: () gives pval = 0.89556 / val = 0.056
Non-significance detected.
Link (V6 -1) -?> V6 (16/21):
Subset 0: () gives pval = 0.59685 / val = 0.222
Non-significance detected.
Link (V6 -2) -?> V6 (17/21):
Subset 0: () gives pval = 0.75751 / val = -0.131
Non-significance detected.
Link (V6 -3) -?> V6 (18/21):
Subset 0: () gives pval = 0.41015 / val = -0.340
Non-significance detected.
Link (V7 -1) -?> V6 (19/21):
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Link (V7 -2) -?> V6 (20/21):
Subset 0: () gives pval = 0.48406 / val = 0.291
Non-significance detected.
Link (V7 -3) -?> V6 (21/21):
Subset 0: () gives pval = 0.81090 / val = -0.102
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Algorithm converged for variable V6
## Variable V7
Iterating through pc_alpha = [0.005]:
# pc_alpha = 0.005 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V7 (1/21):
Subset 0: () gives pval = 0.10602 / val = 0.613
Non-significance detected.
Link (V1 -2) -?> V7 (2/21):
Subset 0: () gives pval = 0.13143 / val = -0.580
Non-significance detected.
Link (V1 -3) -?> V7 (3/21):
Subset 0: () gives pval = 0.20399 / val = -0.503
Non-significance detected.
Link (V2 -1) -?> V7 (4/21):
Subset 0: () gives pval = 0.31711 / val = 0.407
Non-significance detected.
Link (V2 -2) -?> V7 (5/21):
Subset 0: () gives pval = 0.40496 / val = 0.343
Non-significance detected.
Link (V2 -3) -?> V7 (6/21):
Subset 0: () gives pval = 0.49089 / val = -0.287
Non-significance detected.
Link (V3 -1) -?> V7 (7/21):
Subset 0: () gives pval = 0.92032 / val = 0.043
Non-significance detected.
Link (V3 -2) -?> V7 (8/21):
Subset 0: () gives pval = 0.79775 / val = -0.109
Non-significance detected.
Link (V3 -3) -?> V7 (9/21):
Subset 0: () gives pval = 0.75377 / val = 0.133
Non-significance detected.
Link (V4 -1) -?> V7 (10/21):
Subset 0: () gives pval = 0.75703 / val = -0.131
Non-significance detected.
Link (V4 -2) -?> V7 (11/21):
Subset 0: () gives pval = 0.07150 / val = -0.666
Non-significance detected.
Link (V4 -3) -?> V7 (12/21):
Subset 0: () gives pval = 0.87683 / val = 0.066
Non-significance detected.
Link (V5 -1) -?> V7 (13/21):
Subset 0: () gives pval = 0.97094 / val = 0.016
Non-significance detected.
Link (V5 -2) -?> V7 (14/21):
Subset 0: () gives pval = 0.62396 / val = -0.206
Non-significance detected.
Link (V5 -3) -?> V7 (15/21):
Subset 0: () gives pval = 0.16865 / val = 0.538
Non-significance detected.
Link (V6 -1) -?> V7 (16/21):
Subset 0: () gives pval = 0.98554 / val = -0.008
Non-significance detected.
Link (V6 -2) -?> V7 (17/21):
Subset 0: () gives pval = 0.90824 / val = -0.049
Non-significance detected.
Link (V6 -3) -?> V7 (18/21):
Subset 0: () gives pval = 0.13870 / val = 0.572
Non-significance detected.
Link (V7 -1) -?> V7 (19/21):
Subset 0: () gives pval = 0.50733 / val = 0.277
Non-significance detected.
Link (V7 -2) -?> V7 (20/21):
Subset 0: () gives pval = 0.93834 / val = 0.033
Non-significance detected.
Link (V7 -3) -?> V7 (21/21):
Subset 0: () gives pval = 0.92994 / val = -0.037
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V7 has 0 link(s):
Algorithm converged for variable V7
## Resulting lagged parent (super)sets:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Variable V7 has 0 link(s):
##
## Step 2: PC algorithm with contemp. conditions and MCI tests
##
Parameters:
independence test = par_corr
tau_min = 0
tau_max = 3
pc_alpha = 0.005
contemp_collider_rule = majority
conflict_resolution = True
reset_lagged_links = False
max_conds_dim = None
max_conds_py = None
max_conds_px = None
max_conds_px_lagged = None
fdr_method = none
--------------------------
Skeleton discovery phase
--------------------------
Testing contemporaneous condition sets of dimension 0:
Link (V1 0) o?o V2 (1/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V2 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.78838 / val = 0.126
Non-significance detected.
Link (V1 0) o?o V3 (2/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.96748 / val = 0.017
Non-significance detected.
Link (V1 0) o?o V4 (3/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.39632 / val = 0.349
Non-significance detected.
Link (V1 0) o?o V5 (4/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.89723 / val = 0.055
Non-significance detected.
Link (V1 0) o?o V6 (5/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.46578 / val = -0.333
Non-significance detected.
Link (V1 0) o?o V7 (6/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32813 / val = 0.399
Non-significance detected.
Link (V2 0) o?o V1 (7/44):
Already removed.
Link (V2 -2) -?> V2 (8/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -4) ]
Subset 0: () gives pval = 0.00773 / val = -0.887
Non-significance detected.
Link (V2 0) o?o V3 (9/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.11874 / val = -0.644
Non-significance detected.
Link (V2 0) o?o V4 (10/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.64856 / val = 0.212
Non-significance detected.
Link (V2 0) o?o V5 (11/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.33073 / val = 0.434
Non-significance detected.
Link (V2 0) o?o V6 (12/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.49710 / val = 0.349
Non-significance detected.
Link (V2 0) o?o V7 (13/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.93791 / val = -0.037
Non-significance detected.
Link (V3 0) o?o V1 (14/44):
Already removed.
Link (V3 0) o?o V2 (15/44):
Already removed.
Link (V3 0) o?o V4 (16/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.30341 / val = 0.417
Non-significance detected.
Link (V3 0) o?o V5 (17/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.95447 / val = 0.024
Non-significance detected.
Link (V3 0) o?o V6 (18/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.53674 / val = -0.284
Non-significance detected.
Link (V3 0) o?o V7 (19/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.25153 / val = -0.460
Non-significance detected.
Link (V4 0) o?o V1 (20/44):
Already removed.
Link (V4 0) o?o V2 (21/44):
Already removed.
Link (V4 0) o?o V3 (22/44):
Already removed.
Link (V4 0) o?o V5 (23/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.20930 / val = 0.498
Non-significance detected.
Link (V4 0) o?o V6 (24/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.26768 / val = -0.487
Non-significance detected.
Link (V4 0) o?o V7 (25/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.92759 / val = -0.039
Non-significance detected.
Link (V5 0) o?o V1 (26/44):
Already removed.
Link (V5 0) o?o V2 (27/44):
Already removed.
Link (V5 0) o?o V3 (28/44):
Already removed.
Link (V5 0) o?o V4 (29/44):
Already removed.
Link (V5 0) o?o V6 (30/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.38468 / val = 0.392
Non-significance detected.
Link (V5 0) o?o V7 (31/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32066 / val = -0.404
Non-significance detected.
Link (V6 0) o?o V1 (32/44):
Already removed.
Link (V6 0) o?o V2 (33/44):
Already removed.
Link (V6 0) o?o V3 (34/44):
Already removed.
Link (V6 0) o?o V4 (35/44):
Already removed.
Link (V6 0) o?o V5 (36/44):
Already removed.
Link (V6 0) o?o V7 (37/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V7 -1) ]
Subset 0: () gives pval = 0.09642 / val = -0.675
Non-significance detected.
Link (V7 0) o?o V1 (38/44):
Already removed.
Link (V7 0) o?o V2 (39/44):
Already removed.
Link (V7 0) o?o V3 (40/44):
Already removed.
Link (V7 0) o?o V4 (41/44):
Already removed.
Link (V7 0) o?o V5 (42/44):
Already removed.
Link (V7 0) o?o V6 (43/44):
Already removed.
Link (V7 -1) -?> V6 (44/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Updated contemp. adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 0 link(s):
Variable V7 has 0 link(s):
Algorithm converged at p = 0.
----------------------------
Collider orientation phase
----------------------------
contemp_collider_rule = majority
conflict_resolution = True
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
----------------------------
Rule orientation phase
----------------------------
Try rule(s) [1 2 3]
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
## Significant links at alpha = 0.005:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): pval = 0.00000 | val = 0.992
Variable V7 has 0 link(s):
## pc_alpha = 0.01 (3/5):
##
## Step 1: PC1 algorithm for selecting lagged conditions
##
Parameters:
independence test = par_corr
tau_min = 1
tau_max = 3
pc_alpha = [0.01]
max_conds_dim = None
max_combinations = 1
## Variable V1
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V1 (1/21):
Subset 0: () gives pval = 0.86601 / val = -0.072
Non-significance detected.
Link (V1 -2) -?> V1 (2/21):
Subset 0: () gives pval = 0.57469 / val = -0.235
Non-significance detected.
Link (V1 -3) -?> V1 (3/21):
Subset 0: () gives pval = 0.13528 / val = -0.576
Non-significance detected.
Link (V2 -1) -?> V1 (4/21):
Subset 0: () gives pval = 0.08631 / val = 0.642
Non-significance detected.
Link (V2 -2) -?> V1 (5/21):
Subset 0: () gives pval = 1.00000 / val = -0.000
Non-significance detected.
Link (V2 -3) -?> V1 (6/21):
Subset 0: () gives pval = 0.08260 / val = -0.647
Non-significance detected.
Link (V3 -1) -?> V1 (7/21):
Subset 0: () gives pval = 0.30492 / val = -0.416
Non-significance detected.
Link (V3 -2) -?> V1 (8/21):
Subset 0: () gives pval = 0.90322 / val = -0.052
Non-significance detected.
Link (V3 -3) -?> V1 (9/21):
Subset 0: () gives pval = 0.59372 / val = 0.224
Non-significance detected.
Link (V4 -1) -?> V1 (10/21):
Subset 0: () gives pval = 0.08508 / val = -0.644
Non-significance detected.
Link (V4 -2) -?> V1 (11/21):
Subset 0: () gives pval = 0.21081 / val = -0.496
Non-significance detected.
Link (V4 -3) -?> V1 (12/21):
Subset 0: () gives pval = 0.26642 / val = 0.447
Non-significance detected.
Link (V5 -1) -?> V1 (13/21):
Subset 0: () gives pval = 0.36475 / val = -0.372
Non-significance detected.
Link (V5 -2) -?> V1 (14/21):
Subset 0: () gives pval = 0.97472 / val = -0.013
Non-significance detected.
Link (V5 -3) -?> V1 (15/21):
Subset 0: () gives pval = 0.28630 / val = 0.431
Non-significance detected.
Link (V6 -1) -?> V1 (16/21):
Subset 0: () gives pval = 0.69615 / val = -0.165
Non-significance detected.
Link (V6 -2) -?> V1 (17/21):
Subset 0: () gives pval = 0.60470 / val = 0.218
Non-significance detected.
Link (V6 -3) -?> V1 (18/21):
Subset 0: () gives pval = 0.64103 / val = 0.196
Non-significance detected.
Link (V7 -1) -?> V1 (19/21):
Subset 0: () gives pval = 0.32015 / val = 0.405
Non-significance detected.
Link (V7 -2) -?> V1 (20/21):
Subset 0: () gives pval = 0.67332 / val = -0.178
Non-significance detected.
Link (V7 -3) -?> V1 (21/21):
Subset 0: () gives pval = 0.52668 / val = 0.265
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V1 has 0 link(s):
Algorithm converged for variable V1
## Variable V2
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V2 (1/21):
Subset 0: () gives pval = 0.12317 / val = -0.591
Non-significance detected.
Link (V1 -2) -?> V2 (2/21):
Subset 0: () gives pval = 0.87304 / val = 0.068
Non-significance detected.
Link (V1 -3) -?> V2 (3/21):
Subset 0: () gives pval = 0.40658 / val = 0.342
Non-significance detected.
Link (V2 -1) -?> V2 (4/21):
Subset 0: () gives pval = 0.87285 / val = -0.068
Non-significance detected.
Link (V2 -2) -?> V2 (5/21):
Subset 0: () gives pval = 0.00058 / val = -0.938
No conditions of dimension 0 left.
Link (V2 -3) -?> V2 (6/21):
Subset 0: () gives pval = 0.38647 / val = 0.356
Non-significance detected.
Link (V3 -1) -?> V2 (7/21):
Subset 0: () gives pval = 0.18843 / val = -0.518
Non-significance detected.
Link (V3 -2) -?> V2 (8/21):
Subset 0: () gives pval = 0.82124 / val = 0.096
Non-significance detected.
Link (V3 -3) -?> V2 (9/21):
Subset 0: () gives pval = 0.25844 / val = 0.454
Non-significance detected.
Link (V4 -1) -?> V2 (10/21):
Subset 0: () gives pval = 0.08165 / val = -0.649
Non-significance detected.
Link (V4 -2) -?> V2 (11/21):
Subset 0: () gives pval = 0.06607 / val = 0.675
Non-significance detected.
Link (V4 -3) -?> V2 (12/21):
Subset 0: () gives pval = 0.58825 / val = 0.227
Non-significance detected.
Link (V5 -1) -?> V2 (13/21):
Subset 0: () gives pval = 0.38186 / val = -0.359
Non-significance detected.
Link (V5 -2) -?> V2 (14/21):
Subset 0: () gives pval = 0.32916 / val = 0.398
Non-significance detected.
Link (V5 -3) -?> V2 (15/21):
Subset 0: () gives pval = 0.98847 / val = 0.006
Non-significance detected.
Link (V6 -1) -?> V2 (16/21):
Subset 0: () gives pval = 0.32076 / val = 0.404
Non-significance detected.
Link (V6 -2) -?> V2 (17/21):
Subset 0: () gives pval = 0.40538 / val = 0.343
Non-significance detected.
Link (V6 -3) -?> V2 (18/21):
Subset 0: () gives pval = 0.37909 / val = -0.361
Non-significance detected.
Link (V7 -1) -?> V2 (19/21):
Subset 0: () gives pval = 0.96874 / val = -0.017
Non-significance detected.
Link (V7 -2) -?> V2 (20/21):
Subset 0: () gives pval = 0.29908 / val = 0.421
Non-significance detected.
Link (V7 -3) -?> V2 (21/21):
Subset 0: () gives pval = 0.32576 / val = 0.400
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Algorithm converged for variable V2
## Variable V3
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V3 (1/21):
Subset 0: () gives pval = 0.39391 / val = -0.351
Non-significance detected.
Link (V1 -2) -?> V3 (2/21):
Subset 0: () gives pval = 0.75698 / val = -0.131
Non-significance detected.
Link (V1 -3) -?> V3 (3/21):
Subset 0: () gives pval = 0.17237 / val = 0.534
Non-significance detected.
Link (V2 -1) -?> V3 (4/21):
Subset 0: () gives pval = 0.25198 / val = 0.460
Non-significance detected.
Link (V2 -2) -?> V3 (5/21):
Subset 0: () gives pval = 0.81987 / val = -0.097
Non-significance detected.
Link (V2 -3) -?> V3 (6/21):
Subset 0: () gives pval = 0.14919 / val = -0.560
Non-significance detected.
Link (V3 -1) -?> V3 (7/21):
Subset 0: () gives pval = 0.92814 / val = 0.038
Non-significance detected.
Link (V3 -2) -?> V3 (8/21):
Subset 0: () gives pval = 0.55198 / val = -0.249
Non-significance detected.
Link (V3 -3) -?> V3 (9/21):
Subset 0: () gives pval = 0.87647 / val = -0.066
Non-significance detected.
Link (V4 -1) -?> V3 (10/21):
Subset 0: () gives pval = 0.83660 / val = 0.088
Non-significance detected.
Link (V4 -2) -?> V3 (11/21):
Subset 0: () gives pval = 0.92891 / val = 0.038
Non-significance detected.
Link (V4 -3) -?> V3 (12/21):
Subset 0: () gives pval = 0.18176 / val = 0.525
Non-significance detected.
Link (V5 -1) -?> V3 (13/21):
Subset 0: () gives pval = 0.32210 / val = 0.403
Non-significance detected.
Link (V5 -2) -?> V3 (14/21):
Subset 0: () gives pval = 0.67508 / val = -0.177
Non-significance detected.
Link (V5 -3) -?> V3 (15/21):
Subset 0: () gives pval = 0.65106 / val = -0.191
Non-significance detected.
Link (V6 -1) -?> V3 (16/21):
Subset 0: () gives pval = 0.87265 / val = -0.068
Non-significance detected.
Link (V6 -2) -?> V3 (17/21):
Subset 0: () gives pval = 0.73304 / val = 0.144
Non-significance detected.
Link (V6 -3) -?> V3 (18/21):
Subset 0: () gives pval = 0.71062 / val = 0.157
Non-significance detected.
Link (V7 -1) -?> V3 (19/21):
Subset 0: () gives pval = 0.08132 / val = -0.650
Non-significance detected.
Link (V7 -2) -?> V3 (20/21):
Subset 0: () gives pval = 0.65185 / val = -0.190
Non-significance detected.
Link (V7 -3) -?> V3 (21/21):
Subset 0: () gives pval = 0.71587 / val = 0.154
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V3 has 0 link(s):
Algorithm converged for variable V3
## Variable V4
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V4 (1/21):
Subset 0: () gives pval = 0.56354 / val = 0.242
Non-significance detected.
Link (V1 -2) -?> V4 (2/21):
Subset 0: () gives pval = 0.58558 / val = 0.229
Non-significance detected.
Link (V1 -3) -?> V4 (3/21):
Subset 0: () gives pval = 0.96166 / val = -0.020
Non-significance detected.
Link (V2 -1) -?> V4 (4/21):
Subset 0: () gives pval = 0.16299 / val = 0.544
Non-significance detected.
Link (V2 -2) -?> V4 (5/21):
Subset 0: () gives pval = 0.24064 / val = 0.469
Non-significance detected.
Link (V2 -3) -?> V4 (6/21):
Subset 0: () gives pval = 0.06141 / val = -0.684
Non-significance detected.
Link (V3 -1) -?> V4 (7/21):
Subset 0: () gives pval = 0.94919 / val = 0.027
Non-significance detected.
Link (V3 -2) -?> V4 (8/21):
Subset 0: () gives pval = 0.02698 / val = -0.765
Non-significance detected.
Link (V3 -3) -?> V4 (9/21):
Subset 0: () gives pval = 0.35707 / val = -0.377
Non-significance detected.
Link (V4 -1) -?> V4 (10/21):
Subset 0: () gives pval = 0.77024 / val = 0.124
Non-significance detected.
Link (V4 -2) -?> V4 (11/21):
Subset 0: () gives pval = 0.12671 / val = -0.586
Non-significance detected.
Link (V4 -3) -?> V4 (12/21):
Subset 0: () gives pval = 0.87499 / val = -0.067
Non-significance detected.
Link (V5 -1) -?> V4 (13/21):
Subset 0: () gives pval = 0.45958 / val = -0.307
Non-significance detected.
Link (V5 -2) -?> V4 (14/21):
Subset 0: () gives pval = 0.72738 / val = -0.148
Non-significance detected.
Link (V5 -3) -?> V4 (15/21):
Subset 0: () gives pval = 0.29395 / val = -0.425
Non-significance detected.
Link (V6 -1) -?> V4 (16/21):
Subset 0: () gives pval = 0.88424 / val = 0.062
Non-significance detected.
Link (V6 -2) -?> V4 (17/21):
Subset 0: () gives pval = 0.17711 / val = 0.530
Non-significance detected.
Link (V6 -3) -?> V4 (18/21):
Subset 0: () gives pval = 0.81886 / val = 0.097
Non-significance detected.
Link (V7 -1) -?> V4 (19/21):
Subset 0: () gives pval = 0.80817 / val = 0.103
Non-significance detected.
Link (V7 -2) -?> V4 (20/21):
Subset 0: () gives pval = 0.93921 / val = 0.032
Non-significance detected.
Link (V7 -3) -?> V4 (21/21):
Subset 0: () gives pval = 0.21585 / val = 0.492
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V4 has 0 link(s):
Algorithm converged for variable V4
## Variable V5
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V5 (1/21):
Subset 0: () gives pval = 0.37886 / val = -0.362
Non-significance detected.
Link (V1 -2) -?> V5 (2/21):
Subset 0: () gives pval = 0.30644 / val = 0.415
Non-significance detected.
Link (V1 -3) -?> V5 (3/21):
Subset 0: () gives pval = 0.73999 / val = -0.141
Non-significance detected.
Link (V2 -1) -?> V5 (4/21):
Subset 0: () gives pval = 0.95989 / val = -0.021
Non-significance detected.
Link (V2 -2) -?> V5 (5/21):
Subset 0: () gives pval = 0.72633 / val = 0.148
Non-significance detected.
Link (V2 -3) -?> V5 (6/21):
Subset 0: () gives pval = 0.80597 / val = -0.104
Non-significance detected.
Link (V3 -1) -?> V5 (7/21):
Subset 0: () gives pval = 0.42170 / val = 0.332
Non-significance detected.
Link (V3 -2) -?> V5 (8/21):
Subset 0: () gives pval = 0.70342 / val = -0.161
Non-significance detected.
Link (V3 -3) -?> V5 (9/21):
Subset 0: () gives pval = 0.16043 / val = -0.547
Non-significance detected.
Link (V4 -1) -?> V5 (10/21):
Subset 0: () gives pval = 0.85612 / val = 0.077
Non-significance detected.
Link (V4 -2) -?> V5 (11/21):
Subset 0: () gives pval = 0.71488 / val = 0.155
Non-significance detected.
Link (V4 -3) -?> V5 (12/21):
Subset 0: () gives pval = 0.74776 / val = -0.136
Non-significance detected.
Link (V5 -1) -?> V5 (13/21):
Subset 0: () gives pval = 0.12982 / val = -0.582
Non-significance detected.
Link (V5 -2) -?> V5 (14/21):
Subset 0: () gives pval = 0.36498 / val = 0.371
Non-significance detected.
Link (V5 -3) -?> V5 (15/21):
Subset 0: () gives pval = 0.40910 / val = -0.341
Non-significance detected.
Link (V6 -1) -?> V5 (16/21):
Subset 0: () gives pval = 0.38906 / val = -0.354
Non-significance detected.
Link (V6 -2) -?> V5 (17/21):
Subset 0: () gives pval = 0.12547 / val = 0.588
Non-significance detected.
Link (V6 -3) -?> V5 (18/21):
Subset 0: () gives pval = 0.73154 / val = -0.145
Non-significance detected.
Link (V7 -1) -?> V5 (19/21):
Subset 0: () gives pval = 0.94756 / val = 0.028
Non-significance detected.
Link (V7 -2) -?> V5 (20/21):
Subset 0: () gives pval = 0.47394 / val = -0.298
Non-significance detected.
Link (V7 -3) -?> V5 (21/21):
Subset 0: () gives pval = 0.19310 / val = 0.513
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V5 has 0 link(s):
Algorithm converged for variable V5
## Variable V6
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V6 (1/21):
Subset 0: () gives pval = 0.38954 / val = 0.354
Non-significance detected.
Link (V1 -2) -?> V6 (2/21):
Subset 0: () gives pval = 0.13823 / val = 0.572
Non-significance detected.
Link (V1 -3) -?> V6 (3/21):
Subset 0: () gives pval = 0.13173 / val = -0.580
Non-significance detected.
Link (V2 -1) -?> V6 (4/21):
Subset 0: () gives pval = 0.45705 / val = -0.309
Non-significance detected.
Link (V2 -2) -?> V6 (5/21):
Subset 0: () gives pval = 0.59135 / val = 0.225
Non-significance detected.
Link (V2 -3) -?> V6 (6/21):
Subset 0: () gives pval = 0.46932 / val = 0.301
Non-significance detected.
Link (V3 -1) -?> V6 (7/21):
Subset 0: () gives pval = 0.19069 / val = -0.516
Non-significance detected.
Link (V3 -2) -?> V6 (8/21):
Subset 0: () gives pval = 0.81980 / val = 0.097
Non-significance detected.
Link (V3 -3) -?> V6 (9/21):
Subset 0: () gives pval = 0.92754 / val = -0.039
Non-significance detected.
Link (V4 -1) -?> V6 (10/21):
Subset 0: () gives pval = 0.79337 / val = -0.111
Non-significance detected.
Link (V4 -2) -?> V6 (11/21):
Subset 0: () gives pval = 0.42452 / val = -0.330
Non-significance detected.
Link (V4 -3) -?> V6 (12/21):
Subset 0: () gives pval = 0.11568 / val = -0.600
Non-significance detected.
Link (V5 -1) -?> V6 (13/21):
Subset 0: () gives pval = 0.26711 / val = -0.447
Non-significance detected.
Link (V5 -2) -?> V6 (14/21):
Subset 0: () gives pval = 0.73415 / val = -0.144
Non-significance detected.
Link (V5 -3) -?> V6 (15/21):
Subset 0: () gives pval = 0.89556 / val = 0.056
Non-significance detected.
Link (V6 -1) -?> V6 (16/21):
Subset 0: () gives pval = 0.59685 / val = 0.222
Non-significance detected.
Link (V6 -2) -?> V6 (17/21):
Subset 0: () gives pval = 0.75751 / val = -0.131
Non-significance detected.
Link (V6 -3) -?> V6 (18/21):
Subset 0: () gives pval = 0.41015 / val = -0.340
Non-significance detected.
Link (V7 -1) -?> V6 (19/21):
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Link (V7 -2) -?> V6 (20/21):
Subset 0: () gives pval = 0.48406 / val = 0.291
Non-significance detected.
Link (V7 -3) -?> V6 (21/21):
Subset 0: () gives pval = 0.81090 / val = -0.102
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Algorithm converged for variable V6
## Variable V7
Iterating through pc_alpha = [0.01]:
# pc_alpha = 0.01 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V7 (1/21):
Subset 0: () gives pval = 0.10602 / val = 0.613
Non-significance detected.
Link (V1 -2) -?> V7 (2/21):
Subset 0: () gives pval = 0.13143 / val = -0.580
Non-significance detected.
Link (V1 -3) -?> V7 (3/21):
Subset 0: () gives pval = 0.20399 / val = -0.503
Non-significance detected.
Link (V2 -1) -?> V7 (4/21):
Subset 0: () gives pval = 0.31711 / val = 0.407
Non-significance detected.
Link (V2 -2) -?> V7 (5/21):
Subset 0: () gives pval = 0.40496 / val = 0.343
Non-significance detected.
Link (V2 -3) -?> V7 (6/21):
Subset 0: () gives pval = 0.49089 / val = -0.287
Non-significance detected.
Link (V3 -1) -?> V7 (7/21):
Subset 0: () gives pval = 0.92032 / val = 0.043
Non-significance detected.
Link (V3 -2) -?> V7 (8/21):
Subset 0: () gives pval = 0.79775 / val = -0.109
Non-significance detected.
Link (V3 -3) -?> V7 (9/21):
Subset 0: () gives pval = 0.75377 / val = 0.133
Non-significance detected.
Link (V4 -1) -?> V7 (10/21):
Subset 0: () gives pval = 0.75703 / val = -0.131
Non-significance detected.
Link (V4 -2) -?> V7 (11/21):
Subset 0: () gives pval = 0.07150 / val = -0.666
Non-significance detected.
Link (V4 -3) -?> V7 (12/21):
Subset 0: () gives pval = 0.87683 / val = 0.066
Non-significance detected.
Link (V5 -1) -?> V7 (13/21):
Subset 0: () gives pval = 0.97094 / val = 0.016
Non-significance detected.
Link (V5 -2) -?> V7 (14/21):
Subset 0: () gives pval = 0.62396 / val = -0.206
Non-significance detected.
Link (V5 -3) -?> V7 (15/21):
Subset 0: () gives pval = 0.16865 / val = 0.538
Non-significance detected.
Link (V6 -1) -?> V7 (16/21):
Subset 0: () gives pval = 0.98554 / val = -0.008
Non-significance detected.
Link (V6 -2) -?> V7 (17/21):
Subset 0: () gives pval = 0.90824 / val = -0.049
Non-significance detected.
Link (V6 -3) -?> V7 (18/21):
Subset 0: () gives pval = 0.13870 / val = 0.572
Non-significance detected.
Link (V7 -1) -?> V7 (19/21):
Subset 0: () gives pval = 0.50733 / val = 0.277
Non-significance detected.
Link (V7 -2) -?> V7 (20/21):
Subset 0: () gives pval = 0.93834 / val = 0.033
Non-significance detected.
Link (V7 -3) -?> V7 (21/21):
Subset 0: () gives pval = 0.92994 / val = -0.037
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V7 has 0 link(s):
Algorithm converged for variable V7
## Resulting lagged parent (super)sets:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Variable V7 has 0 link(s):
##
## Step 2: PC algorithm with contemp. conditions and MCI tests
##
Parameters:
independence test = par_corr
tau_min = 0
tau_max = 3
pc_alpha = 0.01
contemp_collider_rule = majority
conflict_resolution = True
reset_lagged_links = False
max_conds_dim = None
max_conds_py = None
max_conds_px = None
max_conds_px_lagged = None
fdr_method = none
--------------------------
Skeleton discovery phase
--------------------------
Testing contemporaneous condition sets of dimension 0:
Link (V1 0) o?o V2 (1/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V2 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.78838 / val = 0.126
Non-significance detected.
Link (V1 0) o?o V3 (2/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.96748 / val = 0.017
Non-significance detected.
Link (V1 0) o?o V4 (3/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.39632 / val = 0.349
Non-significance detected.
Link (V1 0) o?o V5 (4/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.89723 / val = 0.055
Non-significance detected.
Link (V1 0) o?o V6 (5/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.46578 / val = -0.333
Non-significance detected.
Link (V1 0) o?o V7 (6/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32813 / val = 0.399
Non-significance detected.
Link (V2 0) o?o V1 (7/44):
Already removed.
Link (V2 -2) -?> V2 (8/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -4) ]
Subset 0: () gives pval = 0.00773 / val = -0.887
No conditions of dimension 0 left.
Link (V2 0) o?o V3 (9/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.11874 / val = -0.644
Non-significance detected.
Link (V2 0) o?o V4 (10/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.64856 / val = 0.212
Non-significance detected.
Link (V2 0) o?o V5 (11/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.33073 / val = 0.434
Non-significance detected.
Link (V2 0) o?o V6 (12/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.49710 / val = 0.349
Non-significance detected.
Link (V2 0) o?o V7 (13/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.93791 / val = -0.037
Non-significance detected.
Link (V3 0) o?o V1 (14/44):
Already removed.
Link (V3 0) o?o V2 (15/44):
Already removed.
Link (V3 0) o?o V4 (16/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.30341 / val = 0.417
Non-significance detected.
Link (V3 0) o?o V5 (17/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.95447 / val = 0.024
Non-significance detected.
Link (V3 0) o?o V6 (18/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.53674 / val = -0.284
Non-significance detected.
Link (V3 0) o?o V7 (19/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.25153 / val = -0.460
Non-significance detected.
Link (V4 0) o?o V1 (20/44):
Already removed.
Link (V4 0) o?o V2 (21/44):
Already removed.
Link (V4 0) o?o V3 (22/44):
Already removed.
Link (V4 0) o?o V5 (23/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.20930 / val = 0.498
Non-significance detected.
Link (V4 0) o?o V6 (24/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.26768 / val = -0.487
Non-significance detected.
Link (V4 0) o?o V7 (25/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.92759 / val = -0.039
Non-significance detected.
Link (V5 0) o?o V1 (26/44):
Already removed.
Link (V5 0) o?o V2 (27/44):
Already removed.
Link (V5 0) o?o V3 (28/44):
Already removed.
Link (V5 0) o?o V4 (29/44):
Already removed.
Link (V5 0) o?o V6 (30/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.38468 / val = 0.392
Non-significance detected.
Link (V5 0) o?o V7 (31/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32066 / val = -0.404
Non-significance detected.
Link (V6 0) o?o V1 (32/44):
Already removed.
Link (V6 0) o?o V2 (33/44):
Already removed.
Link (V6 0) o?o V3 (34/44):
Already removed.
Link (V6 0) o?o V4 (35/44):
Already removed.
Link (V6 0) o?o V5 (36/44):
Already removed.
Link (V6 0) o?o V7 (37/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V7 -1) ]
Subset 0: () gives pval = 0.09642 / val = -0.675
Non-significance detected.
Link (V7 0) o?o V1 (38/44):
Already removed.
Link (V7 0) o?o V2 (39/44):
Already removed.
Link (V7 0) o?o V3 (40/44):
Already removed.
Link (V7 0) o?o V4 (41/44):
Already removed.
Link (V7 0) o?o V5 (42/44):
Already removed.
Link (V7 0) o?o V6 (43/44):
Already removed.
Link (V7 -1) -?> V6 (44/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Updated contemp. adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 0 link(s):
Variable V7 has 0 link(s):
Algorithm converged at p = 0.
----------------------------
Collider orientation phase
----------------------------
contemp_collider_rule = majority
conflict_resolution = True
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2)
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
----------------------------
Rule orientation phase
----------------------------
Try rule(s) [1 2 3]
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2)
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
## Significant links at alpha = 0.01:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): pval = 0.00773 | val = -0.887
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): pval = 0.00000 | val = 0.992
Variable V7 has 0 link(s):
## pc_alpha = 0.025 (4/5):
##
## Step 1: PC1 algorithm for selecting lagged conditions
##
Parameters:
independence test = par_corr
tau_min = 1
tau_max = 3
pc_alpha = [0.025]
max_conds_dim = None
max_combinations = 1
## Variable V1
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V1 (1/21):
Subset 0: () gives pval = 0.86601 / val = -0.072
Non-significance detected.
Link (V1 -2) -?> V1 (2/21):
Subset 0: () gives pval = 0.57469 / val = -0.235
Non-significance detected.
Link (V1 -3) -?> V1 (3/21):
Subset 0: () gives pval = 0.13528 / val = -0.576
Non-significance detected.
Link (V2 -1) -?> V1 (4/21):
Subset 0: () gives pval = 0.08631 / val = 0.642
Non-significance detected.
Link (V2 -2) -?> V1 (5/21):
Subset 0: () gives pval = 1.00000 / val = -0.000
Non-significance detected.
Link (V2 -3) -?> V1 (6/21):
Subset 0: () gives pval = 0.08260 / val = -0.647
Non-significance detected.
Link (V3 -1) -?> V1 (7/21):
Subset 0: () gives pval = 0.30492 / val = -0.416
Non-significance detected.
Link (V3 -2) -?> V1 (8/21):
Subset 0: () gives pval = 0.90322 / val = -0.052
Non-significance detected.
Link (V3 -3) -?> V1 (9/21):
Subset 0: () gives pval = 0.59372 / val = 0.224
Non-significance detected.
Link (V4 -1) -?> V1 (10/21):
Subset 0: () gives pval = 0.08508 / val = -0.644
Non-significance detected.
Link (V4 -2) -?> V1 (11/21):
Subset 0: () gives pval = 0.21081 / val = -0.496
Non-significance detected.
Link (V4 -3) -?> V1 (12/21):
Subset 0: () gives pval = 0.26642 / val = 0.447
Non-significance detected.
Link (V5 -1) -?> V1 (13/21):
Subset 0: () gives pval = 0.36475 / val = -0.372
Non-significance detected.
Link (V5 -2) -?> V1 (14/21):
Subset 0: () gives pval = 0.97472 / val = -0.013
Non-significance detected.
Link (V5 -3) -?> V1 (15/21):
Subset 0: () gives pval = 0.28630 / val = 0.431
Non-significance detected.
Link (V6 -1) -?> V1 (16/21):
Subset 0: () gives pval = 0.69615 / val = -0.165
Non-significance detected.
Link (V6 -2) -?> V1 (17/21):
Subset 0: () gives pval = 0.60470 / val = 0.218
Non-significance detected.
Link (V6 -3) -?> V1 (18/21):
Subset 0: () gives pval = 0.64103 / val = 0.196
Non-significance detected.
Link (V7 -1) -?> V1 (19/21):
Subset 0: () gives pval = 0.32015 / val = 0.405
Non-significance detected.
Link (V7 -2) -?> V1 (20/21):
Subset 0: () gives pval = 0.67332 / val = -0.178
Non-significance detected.
Link (V7 -3) -?> V1 (21/21):
Subset 0: () gives pval = 0.52668 / val = 0.265
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V1 has 0 link(s):
Algorithm converged for variable V1
## Variable V2
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V2 (1/21):
Subset 0: () gives pval = 0.12317 / val = -0.591
Non-significance detected.
Link (V1 -2) -?> V2 (2/21):
Subset 0: () gives pval = 0.87304 / val = 0.068
Non-significance detected.
Link (V1 -3) -?> V2 (3/21):
Subset 0: () gives pval = 0.40658 / val = 0.342
Non-significance detected.
Link (V2 -1) -?> V2 (4/21):
Subset 0: () gives pval = 0.87285 / val = -0.068
Non-significance detected.
Link (V2 -2) -?> V2 (5/21):
Subset 0: () gives pval = 0.00058 / val = -0.938
No conditions of dimension 0 left.
Link (V2 -3) -?> V2 (6/21):
Subset 0: () gives pval = 0.38647 / val = 0.356
Non-significance detected.
Link (V3 -1) -?> V2 (7/21):
Subset 0: () gives pval = 0.18843 / val = -0.518
Non-significance detected.
Link (V3 -2) -?> V2 (8/21):
Subset 0: () gives pval = 0.82124 / val = 0.096
Non-significance detected.
Link (V3 -3) -?> V2 (9/21):
Subset 0: () gives pval = 0.25844 / val = 0.454
Non-significance detected.
Link (V4 -1) -?> V2 (10/21):
Subset 0: () gives pval = 0.08165 / val = -0.649
Non-significance detected.
Link (V4 -2) -?> V2 (11/21):
Subset 0: () gives pval = 0.06607 / val = 0.675
Non-significance detected.
Link (V4 -3) -?> V2 (12/21):
Subset 0: () gives pval = 0.58825 / val = 0.227
Non-significance detected.
Link (V5 -1) -?> V2 (13/21):
Subset 0: () gives pval = 0.38186 / val = -0.359
Non-significance detected.
Link (V5 -2) -?> V2 (14/21):
Subset 0: () gives pval = 0.32916 / val = 0.398
Non-significance detected.
Link (V5 -3) -?> V2 (15/21):
Subset 0: () gives pval = 0.98847 / val = 0.006
Non-significance detected.
Link (V6 -1) -?> V2 (16/21):
Subset 0: () gives pval = 0.32076 / val = 0.404
Non-significance detected.
Link (V6 -2) -?> V2 (17/21):
Subset 0: () gives pval = 0.40538 / val = 0.343
Non-significance detected.
Link (V6 -3) -?> V2 (18/21):
Subset 0: () gives pval = 0.37909 / val = -0.361
Non-significance detected.
Link (V7 -1) -?> V2 (19/21):
Subset 0: () gives pval = 0.96874 / val = -0.017
Non-significance detected.
Link (V7 -2) -?> V2 (20/21):
Subset 0: () gives pval = 0.29908 / val = 0.421
Non-significance detected.
Link (V7 -3) -?> V2 (21/21):
Subset 0: () gives pval = 0.32576 / val = 0.400
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Algorithm converged for variable V2
## Variable V3
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V3 (1/21):
Subset 0: () gives pval = 0.39391 / val = -0.351
Non-significance detected.
Link (V1 -2) -?> V3 (2/21):
Subset 0: () gives pval = 0.75698 / val = -0.131
Non-significance detected.
Link (V1 -3) -?> V3 (3/21):
Subset 0: () gives pval = 0.17237 / val = 0.534
Non-significance detected.
Link (V2 -1) -?> V3 (4/21):
Subset 0: () gives pval = 0.25198 / val = 0.460
Non-significance detected.
Link (V2 -2) -?> V3 (5/21):
Subset 0: () gives pval = 0.81987 / val = -0.097
Non-significance detected.
Link (V2 -3) -?> V3 (6/21):
Subset 0: () gives pval = 0.14919 / val = -0.560
Non-significance detected.
Link (V3 -1) -?> V3 (7/21):
Subset 0: () gives pval = 0.92814 / val = 0.038
Non-significance detected.
Link (V3 -2) -?> V3 (8/21):
Subset 0: () gives pval = 0.55198 / val = -0.249
Non-significance detected.
Link (V3 -3) -?> V3 (9/21):
Subset 0: () gives pval = 0.87647 / val = -0.066
Non-significance detected.
Link (V4 -1) -?> V3 (10/21):
Subset 0: () gives pval = 0.83660 / val = 0.088
Non-significance detected.
Link (V4 -2) -?> V3 (11/21):
Subset 0: () gives pval = 0.92891 / val = 0.038
Non-significance detected.
Link (V4 -3) -?> V3 (12/21):
Subset 0: () gives pval = 0.18176 / val = 0.525
Non-significance detected.
Link (V5 -1) -?> V3 (13/21):
Subset 0: () gives pval = 0.32210 / val = 0.403
Non-significance detected.
Link (V5 -2) -?> V3 (14/21):
Subset 0: () gives pval = 0.67508 / val = -0.177
Non-significance detected.
Link (V5 -3) -?> V3 (15/21):
Subset 0: () gives pval = 0.65106 / val = -0.191
Non-significance detected.
Link (V6 -1) -?> V3 (16/21):
Subset 0: () gives pval = 0.87265 / val = -0.068
Non-significance detected.
Link (V6 -2) -?> V3 (17/21):
Subset 0: () gives pval = 0.73304 / val = 0.144
Non-significance detected.
Link (V6 -3) -?> V3 (18/21):
Subset 0: () gives pval = 0.71062 / val = 0.157
Non-significance detected.
Link (V7 -1) -?> V3 (19/21):
Subset 0: () gives pval = 0.08132 / val = -0.650
Non-significance detected.
Link (V7 -2) -?> V3 (20/21):
Subset 0: () gives pval = 0.65185 / val = -0.190
Non-significance detected.
Link (V7 -3) -?> V3 (21/21):
Subset 0: () gives pval = 0.71587 / val = 0.154
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V3 has 0 link(s):
Algorithm converged for variable V3
## Variable V4
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V4 (1/21):
Subset 0: () gives pval = 0.56354 / val = 0.242
Non-significance detected.
Link (V1 -2) -?> V4 (2/21):
Subset 0: () gives pval = 0.58558 / val = 0.229
Non-significance detected.
Link (V1 -3) -?> V4 (3/21):
Subset 0: () gives pval = 0.96166 / val = -0.020
Non-significance detected.
Link (V2 -1) -?> V4 (4/21):
Subset 0: () gives pval = 0.16299 / val = 0.544
Non-significance detected.
Link (V2 -2) -?> V4 (5/21):
Subset 0: () gives pval = 0.24064 / val = 0.469
Non-significance detected.
Link (V2 -3) -?> V4 (6/21):
Subset 0: () gives pval = 0.06141 / val = -0.684
Non-significance detected.
Link (V3 -1) -?> V4 (7/21):
Subset 0: () gives pval = 0.94919 / val = 0.027
Non-significance detected.
Link (V3 -2) -?> V4 (8/21):
Subset 0: () gives pval = 0.02698 / val = -0.765
Non-significance detected.
Link (V3 -3) -?> V4 (9/21):
Subset 0: () gives pval = 0.35707 / val = -0.377
Non-significance detected.
Link (V4 -1) -?> V4 (10/21):
Subset 0: () gives pval = 0.77024 / val = 0.124
Non-significance detected.
Link (V4 -2) -?> V4 (11/21):
Subset 0: () gives pval = 0.12671 / val = -0.586
Non-significance detected.
Link (V4 -3) -?> V4 (12/21):
Subset 0: () gives pval = 0.87499 / val = -0.067
Non-significance detected.
Link (V5 -1) -?> V4 (13/21):
Subset 0: () gives pval = 0.45958 / val = -0.307
Non-significance detected.
Link (V5 -2) -?> V4 (14/21):
Subset 0: () gives pval = 0.72738 / val = -0.148
Non-significance detected.
Link (V5 -3) -?> V4 (15/21):
Subset 0: () gives pval = 0.29395 / val = -0.425
Non-significance detected.
Link (V6 -1) -?> V4 (16/21):
Subset 0: () gives pval = 0.88424 / val = 0.062
Non-significance detected.
Link (V6 -2) -?> V4 (17/21):
Subset 0: () gives pval = 0.17711 / val = 0.530
Non-significance detected.
Link (V6 -3) -?> V4 (18/21):
Subset 0: () gives pval = 0.81886 / val = 0.097
Non-significance detected.
Link (V7 -1) -?> V4 (19/21):
Subset 0: () gives pval = 0.80817 / val = 0.103
Non-significance detected.
Link (V7 -2) -?> V4 (20/21):
Subset 0: () gives pval = 0.93921 / val = 0.032
Non-significance detected.
Link (V7 -3) -?> V4 (21/21):
Subset 0: () gives pval = 0.21585 / val = 0.492
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V4 has 0 link(s):
Algorithm converged for variable V4
## Variable V5
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V5 (1/21):
Subset 0: () gives pval = 0.37886 / val = -0.362
Non-significance detected.
Link (V1 -2) -?> V5 (2/21):
Subset 0: () gives pval = 0.30644 / val = 0.415
Non-significance detected.
Link (V1 -3) -?> V5 (3/21):
Subset 0: () gives pval = 0.73999 / val = -0.141
Non-significance detected.
Link (V2 -1) -?> V5 (4/21):
Subset 0: () gives pval = 0.95989 / val = -0.021
Non-significance detected.
Link (V2 -2) -?> V5 (5/21):
Subset 0: () gives pval = 0.72633 / val = 0.148
Non-significance detected.
Link (V2 -3) -?> V5 (6/21):
Subset 0: () gives pval = 0.80597 / val = -0.104
Non-significance detected.
Link (V3 -1) -?> V5 (7/21):
Subset 0: () gives pval = 0.42170 / val = 0.332
Non-significance detected.
Link (V3 -2) -?> V5 (8/21):
Subset 0: () gives pval = 0.70342 / val = -0.161
Non-significance detected.
Link (V3 -3) -?> V5 (9/21):
Subset 0: () gives pval = 0.16043 / val = -0.547
Non-significance detected.
Link (V4 -1) -?> V5 (10/21):
Subset 0: () gives pval = 0.85612 / val = 0.077
Non-significance detected.
Link (V4 -2) -?> V5 (11/21):
Subset 0: () gives pval = 0.71488 / val = 0.155
Non-significance detected.
Link (V4 -3) -?> V5 (12/21):
Subset 0: () gives pval = 0.74776 / val = -0.136
Non-significance detected.
Link (V5 -1) -?> V5 (13/21):
Subset 0: () gives pval = 0.12982 / val = -0.582
Non-significance detected.
Link (V5 -2) -?> V5 (14/21):
Subset 0: () gives pval = 0.36498 / val = 0.371
Non-significance detected.
Link (V5 -3) -?> V5 (15/21):
Subset 0: () gives pval = 0.40910 / val = -0.341
Non-significance detected.
Link (V6 -1) -?> V5 (16/21):
Subset 0: () gives pval = 0.38906 / val = -0.354
Non-significance detected.
Link (V6 -2) -?> V5 (17/21):
Subset 0: () gives pval = 0.12547 / val = 0.588
Non-significance detected.
Link (V6 -3) -?> V5 (18/21):
Subset 0: () gives pval = 0.73154 / val = -0.145
Non-significance detected.
Link (V7 -1) -?> V5 (19/21):
Subset 0: () gives pval = 0.94756 / val = 0.028
Non-significance detected.
Link (V7 -2) -?> V5 (20/21):
Subset 0: () gives pval = 0.47394 / val = -0.298
Non-significance detected.
Link (V7 -3) -?> V5 (21/21):
Subset 0: () gives pval = 0.19310 / val = 0.513
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V5 has 0 link(s):
Algorithm converged for variable V5
## Variable V6
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V6 (1/21):
Subset 0: () gives pval = 0.38954 / val = 0.354
Non-significance detected.
Link (V1 -2) -?> V6 (2/21):
Subset 0: () gives pval = 0.13823 / val = 0.572
Non-significance detected.
Link (V1 -3) -?> V6 (3/21):
Subset 0: () gives pval = 0.13173 / val = -0.580
Non-significance detected.
Link (V2 -1) -?> V6 (4/21):
Subset 0: () gives pval = 0.45705 / val = -0.309
Non-significance detected.
Link (V2 -2) -?> V6 (5/21):
Subset 0: () gives pval = 0.59135 / val = 0.225
Non-significance detected.
Link (V2 -3) -?> V6 (6/21):
Subset 0: () gives pval = 0.46932 / val = 0.301
Non-significance detected.
Link (V3 -1) -?> V6 (7/21):
Subset 0: () gives pval = 0.19069 / val = -0.516
Non-significance detected.
Link (V3 -2) -?> V6 (8/21):
Subset 0: () gives pval = 0.81980 / val = 0.097
Non-significance detected.
Link (V3 -3) -?> V6 (9/21):
Subset 0: () gives pval = 0.92754 / val = -0.039
Non-significance detected.
Link (V4 -1) -?> V6 (10/21):
Subset 0: () gives pval = 0.79337 / val = -0.111
Non-significance detected.
Link (V4 -2) -?> V6 (11/21):
Subset 0: () gives pval = 0.42452 / val = -0.330
Non-significance detected.
Link (V4 -3) -?> V6 (12/21):
Subset 0: () gives pval = 0.11568 / val = -0.600
Non-significance detected.
Link (V5 -1) -?> V6 (13/21):
Subset 0: () gives pval = 0.26711 / val = -0.447
Non-significance detected.
Link (V5 -2) -?> V6 (14/21):
Subset 0: () gives pval = 0.73415 / val = -0.144
Non-significance detected.
Link (V5 -3) -?> V6 (15/21):
Subset 0: () gives pval = 0.89556 / val = 0.056
Non-significance detected.
Link (V6 -1) -?> V6 (16/21):
Subset 0: () gives pval = 0.59685 / val = 0.222
Non-significance detected.
Link (V6 -2) -?> V6 (17/21):
Subset 0: () gives pval = 0.75751 / val = -0.131
Non-significance detected.
Link (V6 -3) -?> V6 (18/21):
Subset 0: () gives pval = 0.41015 / val = -0.340
Non-significance detected.
Link (V7 -1) -?> V6 (19/21):
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Link (V7 -2) -?> V6 (20/21):
Subset 0: () gives pval = 0.48406 / val = 0.291
Non-significance detected.
Link (V7 -3) -?> V6 (21/21):
Subset 0: () gives pval = 0.81090 / val = -0.102
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Algorithm converged for variable V6
## Variable V7
Iterating through pc_alpha = [0.025]:
# pc_alpha = 0.025 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V7 (1/21):
Subset 0: () gives pval = 0.10602 / val = 0.613
Non-significance detected.
Link (V1 -2) -?> V7 (2/21):
Subset 0: () gives pval = 0.13143 / val = -0.580
Non-significance detected.
Link (V1 -3) -?> V7 (3/21):
Subset 0: () gives pval = 0.20399 / val = -0.503
Non-significance detected.
Link (V2 -1) -?> V7 (4/21):
Subset 0: () gives pval = 0.31711 / val = 0.407
Non-significance detected.
Link (V2 -2) -?> V7 (5/21):
Subset 0: () gives pval = 0.40496 / val = 0.343
Non-significance detected.
Link (V2 -3) -?> V7 (6/21):
Subset 0: () gives pval = 0.49089 / val = -0.287
Non-significance detected.
Link (V3 -1) -?> V7 (7/21):
Subset 0: () gives pval = 0.92032 / val = 0.043
Non-significance detected.
Link (V3 -2) -?> V7 (8/21):
Subset 0: () gives pval = 0.79775 / val = -0.109
Non-significance detected.
Link (V3 -3) -?> V7 (9/21):
Subset 0: () gives pval = 0.75377 / val = 0.133
Non-significance detected.
Link (V4 -1) -?> V7 (10/21):
Subset 0: () gives pval = 0.75703 / val = -0.131
Non-significance detected.
Link (V4 -2) -?> V7 (11/21):
Subset 0: () gives pval = 0.07150 / val = -0.666
Non-significance detected.
Link (V4 -3) -?> V7 (12/21):
Subset 0: () gives pval = 0.87683 / val = 0.066
Non-significance detected.
Link (V5 -1) -?> V7 (13/21):
Subset 0: () gives pval = 0.97094 / val = 0.016
Non-significance detected.
Link (V5 -2) -?> V7 (14/21):
Subset 0: () gives pval = 0.62396 / val = -0.206
Non-significance detected.
Link (V5 -3) -?> V7 (15/21):
Subset 0: () gives pval = 0.16865 / val = 0.538
Non-significance detected.
Link (V6 -1) -?> V7 (16/21):
Subset 0: () gives pval = 0.98554 / val = -0.008
Non-significance detected.
Link (V6 -2) -?> V7 (17/21):
Subset 0: () gives pval = 0.90824 / val = -0.049
Non-significance detected.
Link (V6 -3) -?> V7 (18/21):
Subset 0: () gives pval = 0.13870 / val = 0.572
Non-significance detected.
Link (V7 -1) -?> V7 (19/21):
Subset 0: () gives pval = 0.50733 / val = 0.277
Non-significance detected.
Link (V7 -2) -?> V7 (20/21):
Subset 0: () gives pval = 0.93834 / val = 0.033
Non-significance detected.
Link (V7 -3) -?> V7 (21/21):
Subset 0: () gives pval = 0.92994 / val = -0.037
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V7 has 0 link(s):
Algorithm converged for variable V7
## Resulting lagged parent (super)sets:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Variable V7 has 0 link(s):
##
## Step 2: PC algorithm with contemp. conditions and MCI tests
##
Parameters:
independence test = par_corr
tau_min = 0
tau_max = 3
pc_alpha = 0.025
contemp_collider_rule = majority
conflict_resolution = True
reset_lagged_links = False
max_conds_dim = None
max_conds_py = None
max_conds_px = None
max_conds_px_lagged = None
fdr_method = none
--------------------------
Skeleton discovery phase
--------------------------
Testing contemporaneous condition sets of dimension 0:
Link (V1 0) o?o V2 (1/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V2 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.78838 / val = 0.126
Non-significance detected.
Link (V1 0) o?o V3 (2/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.96748 / val = 0.017
Non-significance detected.
Link (V1 0) o?o V4 (3/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.39632 / val = 0.349
Non-significance detected.
Link (V1 0) o?o V5 (4/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.89723 / val = 0.055
Non-significance detected.
Link (V1 0) o?o V6 (5/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.46578 / val = -0.333
Non-significance detected.
Link (V1 0) o?o V7 (6/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32813 / val = 0.399
Non-significance detected.
Link (V2 0) o?o V1 (7/44):
Already removed.
Link (V2 -2) -?> V2 (8/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -4) ]
Subset 0: () gives pval = 0.00773 / val = -0.887
No conditions of dimension 0 left.
Link (V2 0) o?o V3 (9/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.11874 / val = -0.644
Non-significance detected.
Link (V2 0) o?o V4 (10/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.64856 / val = 0.212
Non-significance detected.
Link (V2 0) o?o V5 (11/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.33073 / val = 0.434
Non-significance detected.
Link (V2 0) o?o V6 (12/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.49710 / val = 0.349
Non-significance detected.
Link (V2 0) o?o V7 (13/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.93791 / val = -0.037
Non-significance detected.
Link (V3 0) o?o V1 (14/44):
Already removed.
Link (V3 0) o?o V2 (15/44):
Already removed.
Link (V3 0) o?o V4 (16/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.30341 / val = 0.417
Non-significance detected.
Link (V3 0) o?o V5 (17/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.95447 / val = 0.024
Non-significance detected.
Link (V3 0) o?o V6 (18/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.53674 / val = -0.284
Non-significance detected.
Link (V3 0) o?o V7 (19/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.25153 / val = -0.460
Non-significance detected.
Link (V4 0) o?o V1 (20/44):
Already removed.
Link (V4 0) o?o V2 (21/44):
Already removed.
Link (V4 0) o?o V3 (22/44):
Already removed.
Link (V4 0) o?o V5 (23/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.20930 / val = 0.498
Non-significance detected.
Link (V4 0) o?o V6 (24/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.26768 / val = -0.487
Non-significance detected.
Link (V4 0) o?o V7 (25/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.92759 / val = -0.039
Non-significance detected.
Link (V5 0) o?o V1 (26/44):
Already removed.
Link (V5 0) o?o V2 (27/44):
Already removed.
Link (V5 0) o?o V3 (28/44):
Already removed.
Link (V5 0) o?o V4 (29/44):
Already removed.
Link (V5 0) o?o V6 (30/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.38468 / val = 0.392
Non-significance detected.
Link (V5 0) o?o V7 (31/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32066 / val = -0.404
Non-significance detected.
Link (V6 0) o?o V1 (32/44):
Already removed.
Link (V6 0) o?o V2 (33/44):
Already removed.
Link (V6 0) o?o V3 (34/44):
Already removed.
Link (V6 0) o?o V4 (35/44):
Already removed.
Link (V6 0) o?o V5 (36/44):
Already removed.
Link (V6 0) o?o V7 (37/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V7 -1) ]
Subset 0: () gives pval = 0.09642 / val = -0.675
Non-significance detected.
Link (V7 0) o?o V1 (38/44):
Already removed.
Link (V7 0) o?o V2 (39/44):
Already removed.
Link (V7 0) o?o V3 (40/44):
Already removed.
Link (V7 0) o?o V4 (41/44):
Already removed.
Link (V7 0) o?o V5 (42/44):
Already removed.
Link (V7 0) o?o V6 (43/44):
Already removed.
Link (V7 -1) -?> V6 (44/44):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Updated contemp. adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 0 link(s):
Variable V7 has 0 link(s):
Algorithm converged at p = 0.
----------------------------
Collider orientation phase
----------------------------
contemp_collider_rule = majority
conflict_resolution = True
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2)
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
----------------------------
Rule orientation phase
----------------------------
Try rule(s) [1 2 3]
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2)
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
## Significant links at alpha = 0.025:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): pval = 0.00773 | val = -0.887
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): pval = 0.00000 | val = 0.992
Variable V7 has 0 link(s):
## pc_alpha = 0.05 (5/5):
##
## Step 1: PC1 algorithm for selecting lagged conditions
##
Parameters:
independence test = par_corr
tau_min = 1
tau_max = 3
pc_alpha = [0.05]
max_conds_dim = None
max_combinations = 1
## Variable V1
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V1 (1/21):
Subset 0: () gives pval = 0.86601 / val = -0.072
Non-significance detected.
Link (V1 -2) -?> V1 (2/21):
Subset 0: () gives pval = 0.57469 / val = -0.235
Non-significance detected.
Link (V1 -3) -?> V1 (3/21):
Subset 0: () gives pval = 0.13528 / val = -0.576
Non-significance detected.
Link (V2 -1) -?> V1 (4/21):
Subset 0: () gives pval = 0.08631 / val = 0.642
Non-significance detected.
Link (V2 -2) -?> V1 (5/21):
Subset 0: () gives pval = 1.00000 / val = -0.000
Non-significance detected.
Link (V2 -3) -?> V1 (6/21):
Subset 0: () gives pval = 0.08260 / val = -0.647
Non-significance detected.
Link (V3 -1) -?> V1 (7/21):
Subset 0: () gives pval = 0.30492 / val = -0.416
Non-significance detected.
Link (V3 -2) -?> V1 (8/21):
Subset 0: () gives pval = 0.90322 / val = -0.052
Non-significance detected.
Link (V3 -3) -?> V1 (9/21):
Subset 0: () gives pval = 0.59372 / val = 0.224
Non-significance detected.
Link (V4 -1) -?> V1 (10/21):
Subset 0: () gives pval = 0.08508 / val = -0.644
Non-significance detected.
Link (V4 -2) -?> V1 (11/21):
Subset 0: () gives pval = 0.21081 / val = -0.496
Non-significance detected.
Link (V4 -3) -?> V1 (12/21):
Subset 0: () gives pval = 0.26642 / val = 0.447
Non-significance detected.
Link (V5 -1) -?> V1 (13/21):
Subset 0: () gives pval = 0.36475 / val = -0.372
Non-significance detected.
Link (V5 -2) -?> V1 (14/21):
Subset 0: () gives pval = 0.97472 / val = -0.013
Non-significance detected.
Link (V5 -3) -?> V1 (15/21):
Subset 0: () gives pval = 0.28630 / val = 0.431
Non-significance detected.
Link (V6 -1) -?> V1 (16/21):
Subset 0: () gives pval = 0.69615 / val = -0.165
Non-significance detected.
Link (V6 -2) -?> V1 (17/21):
Subset 0: () gives pval = 0.60470 / val = 0.218
Non-significance detected.
Link (V6 -3) -?> V1 (18/21):
Subset 0: () gives pval = 0.64103 / val = 0.196
Non-significance detected.
Link (V7 -1) -?> V1 (19/21):
Subset 0: () gives pval = 0.32015 / val = 0.405
Non-significance detected.
Link (V7 -2) -?> V1 (20/21):
Subset 0: () gives pval = 0.67332 / val = -0.178
Non-significance detected.
Link (V7 -3) -?> V1 (21/21):
Subset 0: () gives pval = 0.52668 / val = 0.265
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V1 has 0 link(s):
Algorithm converged for variable V1
## Variable V2
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V2 (1/21):
Subset 0: () gives pval = 0.12317 / val = -0.591
Non-significance detected.
Link (V1 -2) -?> V2 (2/21):
Subset 0: () gives pval = 0.87304 / val = 0.068
Non-significance detected.
Link (V1 -3) -?> V2 (3/21):
Subset 0: () gives pval = 0.40658 / val = 0.342
Non-significance detected.
Link (V2 -1) -?> V2 (4/21):
Subset 0: () gives pval = 0.87285 / val = -0.068
Non-significance detected.
Link (V2 -2) -?> V2 (5/21):
Subset 0: () gives pval = 0.00058 / val = -0.938
No conditions of dimension 0 left.
Link (V2 -3) -?> V2 (6/21):
Subset 0: () gives pval = 0.38647 / val = 0.356
Non-significance detected.
Link (V3 -1) -?> V2 (7/21):
Subset 0: () gives pval = 0.18843 / val = -0.518
Non-significance detected.
Link (V3 -2) -?> V2 (8/21):
Subset 0: () gives pval = 0.82124 / val = 0.096
Non-significance detected.
Link (V3 -3) -?> V2 (9/21):
Subset 0: () gives pval = 0.25844 / val = 0.454
Non-significance detected.
Link (V4 -1) -?> V2 (10/21):
Subset 0: () gives pval = 0.08165 / val = -0.649
Non-significance detected.
Link (V4 -2) -?> V2 (11/21):
Subset 0: () gives pval = 0.06607 / val = 0.675
Non-significance detected.
Link (V4 -3) -?> V2 (12/21):
Subset 0: () gives pval = 0.58825 / val = 0.227
Non-significance detected.
Link (V5 -1) -?> V2 (13/21):
Subset 0: () gives pval = 0.38186 / val = -0.359
Non-significance detected.
Link (V5 -2) -?> V2 (14/21):
Subset 0: () gives pval = 0.32916 / val = 0.398
Non-significance detected.
Link (V5 -3) -?> V2 (15/21):
Subset 0: () gives pval = 0.98847 / val = 0.006
Non-significance detected.
Link (V6 -1) -?> V2 (16/21):
Subset 0: () gives pval = 0.32076 / val = 0.404
Non-significance detected.
Link (V6 -2) -?> V2 (17/21):
Subset 0: () gives pval = 0.40538 / val = 0.343
Non-significance detected.
Link (V6 -3) -?> V2 (18/21):
Subset 0: () gives pval = 0.37909 / val = -0.361
Non-significance detected.
Link (V7 -1) -?> V2 (19/21):
Subset 0: () gives pval = 0.96874 / val = -0.017
Non-significance detected.
Link (V7 -2) -?> V2 (20/21):
Subset 0: () gives pval = 0.29908 / val = 0.421
Non-significance detected.
Link (V7 -3) -?> V2 (21/21):
Subset 0: () gives pval = 0.32576 / val = 0.400
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Algorithm converged for variable V2
## Variable V3
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V3 (1/21):
Subset 0: () gives pval = 0.39391 / val = -0.351
Non-significance detected.
Link (V1 -2) -?> V3 (2/21):
Subset 0: () gives pval = 0.75698 / val = -0.131
Non-significance detected.
Link (V1 -3) -?> V3 (3/21):
Subset 0: () gives pval = 0.17237 / val = 0.534
Non-significance detected.
Link (V2 -1) -?> V3 (4/21):
Subset 0: () gives pval = 0.25198 / val = 0.460
Non-significance detected.
Link (V2 -2) -?> V3 (5/21):
Subset 0: () gives pval = 0.81987 / val = -0.097
Non-significance detected.
Link (V2 -3) -?> V3 (6/21):
Subset 0: () gives pval = 0.14919 / val = -0.560
Non-significance detected.
Link (V3 -1) -?> V3 (7/21):
Subset 0: () gives pval = 0.92814 / val = 0.038
Non-significance detected.
Link (V3 -2) -?> V3 (8/21):
Subset 0: () gives pval = 0.55198 / val = -0.249
Non-significance detected.
Link (V3 -3) -?> V3 (9/21):
Subset 0: () gives pval = 0.87647 / val = -0.066
Non-significance detected.
Link (V4 -1) -?> V3 (10/21):
Subset 0: () gives pval = 0.83660 / val = 0.088
Non-significance detected.
Link (V4 -2) -?> V3 (11/21):
Subset 0: () gives pval = 0.92891 / val = 0.038
Non-significance detected.
Link (V4 -3) -?> V3 (12/21):
Subset 0: () gives pval = 0.18176 / val = 0.525
Non-significance detected.
Link (V5 -1) -?> V3 (13/21):
Subset 0: () gives pval = 0.32210 / val = 0.403
Non-significance detected.
Link (V5 -2) -?> V3 (14/21):
Subset 0: () gives pval = 0.67508 / val = -0.177
Non-significance detected.
Link (V5 -3) -?> V3 (15/21):
Subset 0: () gives pval = 0.65106 / val = -0.191
Non-significance detected.
Link (V6 -1) -?> V3 (16/21):
Subset 0: () gives pval = 0.87265 / val = -0.068
Non-significance detected.
Link (V6 -2) -?> V3 (17/21):
Subset 0: () gives pval = 0.73304 / val = 0.144
Non-significance detected.
Link (V6 -3) -?> V3 (18/21):
Subset 0: () gives pval = 0.71062 / val = 0.157
Non-significance detected.
Link (V7 -1) -?> V3 (19/21):
Subset 0: () gives pval = 0.08132 / val = -0.650
Non-significance detected.
Link (V7 -2) -?> V3 (20/21):
Subset 0: () gives pval = 0.65185 / val = -0.190
Non-significance detected.
Link (V7 -3) -?> V3 (21/21):
Subset 0: () gives pval = 0.71587 / val = 0.154
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V3 has 0 link(s):
Algorithm converged for variable V3
## Variable V4
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V4 (1/21):
Subset 0: () gives pval = 0.56354 / val = 0.242
Non-significance detected.
Link (V1 -2) -?> V4 (2/21):
Subset 0: () gives pval = 0.58558 / val = 0.229
Non-significance detected.
Link (V1 -3) -?> V4 (3/21):
Subset 0: () gives pval = 0.96166 / val = -0.020
Non-significance detected.
Link (V2 -1) -?> V4 (4/21):
Subset 0: () gives pval = 0.16299 / val = 0.544
Non-significance detected.
Link (V2 -2) -?> V4 (5/21):
Subset 0: () gives pval = 0.24064 / val = 0.469
Non-significance detected.
Link (V2 -3) -?> V4 (6/21):
Subset 0: () gives pval = 0.06141 / val = -0.684
Non-significance detected.
Link (V3 -1) -?> V4 (7/21):
Subset 0: () gives pval = 0.94919 / val = 0.027
Non-significance detected.
Link (V3 -2) -?> V4 (8/21):
Subset 0: () gives pval = 0.02698 / val = -0.765
No conditions of dimension 0 left.
Link (V3 -3) -?> V4 (9/21):
Subset 0: () gives pval = 0.35707 / val = -0.377
Non-significance detected.
Link (V4 -1) -?> V4 (10/21):
Subset 0: () gives pval = 0.77024 / val = 0.124
Non-significance detected.
Link (V4 -2) -?> V4 (11/21):
Subset 0: () gives pval = 0.12671 / val = -0.586
Non-significance detected.
Link (V4 -3) -?> V4 (12/21):
Subset 0: () gives pval = 0.87499 / val = -0.067
Non-significance detected.
Link (V5 -1) -?> V4 (13/21):
Subset 0: () gives pval = 0.45958 / val = -0.307
Non-significance detected.
Link (V5 -2) -?> V4 (14/21):
Subset 0: () gives pval = 0.72738 / val = -0.148
Non-significance detected.
Link (V5 -3) -?> V4 (15/21):
Subset 0: () gives pval = 0.29395 / val = -0.425
Non-significance detected.
Link (V6 -1) -?> V4 (16/21):
Subset 0: () gives pval = 0.88424 / val = 0.062
Non-significance detected.
Link (V6 -2) -?> V4 (17/21):
Subset 0: () gives pval = 0.17711 / val = 0.530
Non-significance detected.
Link (V6 -3) -?> V4 (18/21):
Subset 0: () gives pval = 0.81886 / val = 0.097
Non-significance detected.
Link (V7 -1) -?> V4 (19/21):
Subset 0: () gives pval = 0.80817 / val = 0.103
Non-significance detected.
Link (V7 -2) -?> V4 (20/21):
Subset 0: () gives pval = 0.93921 / val = 0.032
Non-significance detected.
Link (V7 -3) -?> V4 (21/21):
Subset 0: () gives pval = 0.21585 / val = 0.492
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V4 has 1 link(s):
(V3 -2): max_pval = 0.02698, |min_val| = 0.765
Algorithm converged for variable V4
## Variable V5
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V5 (1/21):
Subset 0: () gives pval = 0.37886 / val = -0.362
Non-significance detected.
Link (V1 -2) -?> V5 (2/21):
Subset 0: () gives pval = 0.30644 / val = 0.415
Non-significance detected.
Link (V1 -3) -?> V5 (3/21):
Subset 0: () gives pval = 0.73999 / val = -0.141
Non-significance detected.
Link (V2 -1) -?> V5 (4/21):
Subset 0: () gives pval = 0.95989 / val = -0.021
Non-significance detected.
Link (V2 -2) -?> V5 (5/21):
Subset 0: () gives pval = 0.72633 / val = 0.148
Non-significance detected.
Link (V2 -3) -?> V5 (6/21):
Subset 0: () gives pval = 0.80597 / val = -0.104
Non-significance detected.
Link (V3 -1) -?> V5 (7/21):
Subset 0: () gives pval = 0.42170 / val = 0.332
Non-significance detected.
Link (V3 -2) -?> V5 (8/21):
Subset 0: () gives pval = 0.70342 / val = -0.161
Non-significance detected.
Link (V3 -3) -?> V5 (9/21):
Subset 0: () gives pval = 0.16043 / val = -0.547
Non-significance detected.
Link (V4 -1) -?> V5 (10/21):
Subset 0: () gives pval = 0.85612 / val = 0.077
Non-significance detected.
Link (V4 -2) -?> V5 (11/21):
Subset 0: () gives pval = 0.71488 / val = 0.155
Non-significance detected.
Link (V4 -3) -?> V5 (12/21):
Subset 0: () gives pval = 0.74776 / val = -0.136
Non-significance detected.
Link (V5 -1) -?> V5 (13/21):
Subset 0: () gives pval = 0.12982 / val = -0.582
Non-significance detected.
Link (V5 -2) -?> V5 (14/21):
Subset 0: () gives pval = 0.36498 / val = 0.371
Non-significance detected.
Link (V5 -3) -?> V5 (15/21):
Subset 0: () gives pval = 0.40910 / val = -0.341
Non-significance detected.
Link (V6 -1) -?> V5 (16/21):
Subset 0: () gives pval = 0.38906 / val = -0.354
Non-significance detected.
Link (V6 -2) -?> V5 (17/21):
Subset 0: () gives pval = 0.12547 / val = 0.588
Non-significance detected.
Link (V6 -3) -?> V5 (18/21):
Subset 0: () gives pval = 0.73154 / val = -0.145
Non-significance detected.
Link (V7 -1) -?> V5 (19/21):
Subset 0: () gives pval = 0.94756 / val = 0.028
Non-significance detected.
Link (V7 -2) -?> V5 (20/21):
Subset 0: () gives pval = 0.47394 / val = -0.298
Non-significance detected.
Link (V7 -3) -?> V5 (21/21):
Subset 0: () gives pval = 0.19310 / val = 0.513
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V5 has 0 link(s):
Algorithm converged for variable V5
## Variable V6
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V6 (1/21):
Subset 0: () gives pval = 0.38954 / val = 0.354
Non-significance detected.
Link (V1 -2) -?> V6 (2/21):
Subset 0: () gives pval = 0.13823 / val = 0.572
Non-significance detected.
Link (V1 -3) -?> V6 (3/21):
Subset 0: () gives pval = 0.13173 / val = -0.580
Non-significance detected.
Link (V2 -1) -?> V6 (4/21):
Subset 0: () gives pval = 0.45705 / val = -0.309
Non-significance detected.
Link (V2 -2) -?> V6 (5/21):
Subset 0: () gives pval = 0.59135 / val = 0.225
Non-significance detected.
Link (V2 -3) -?> V6 (6/21):
Subset 0: () gives pval = 0.46932 / val = 0.301
Non-significance detected.
Link (V3 -1) -?> V6 (7/21):
Subset 0: () gives pval = 0.19069 / val = -0.516
Non-significance detected.
Link (V3 -2) -?> V6 (8/21):
Subset 0: () gives pval = 0.81980 / val = 0.097
Non-significance detected.
Link (V3 -3) -?> V6 (9/21):
Subset 0: () gives pval = 0.92754 / val = -0.039
Non-significance detected.
Link (V4 -1) -?> V6 (10/21):
Subset 0: () gives pval = 0.79337 / val = -0.111
Non-significance detected.
Link (V4 -2) -?> V6 (11/21):
Subset 0: () gives pval = 0.42452 / val = -0.330
Non-significance detected.
Link (V4 -3) -?> V6 (12/21):
Subset 0: () gives pval = 0.11568 / val = -0.600
Non-significance detected.
Link (V5 -1) -?> V6 (13/21):
Subset 0: () gives pval = 0.26711 / val = -0.447
Non-significance detected.
Link (V5 -2) -?> V6 (14/21):
Subset 0: () gives pval = 0.73415 / val = -0.144
Non-significance detected.
Link (V5 -3) -?> V6 (15/21):
Subset 0: () gives pval = 0.89556 / val = 0.056
Non-significance detected.
Link (V6 -1) -?> V6 (16/21):
Subset 0: () gives pval = 0.59685 / val = 0.222
Non-significance detected.
Link (V6 -2) -?> V6 (17/21):
Subset 0: () gives pval = 0.75751 / val = -0.131
Non-significance detected.
Link (V6 -3) -?> V6 (18/21):
Subset 0: () gives pval = 0.41015 / val = -0.340
Non-significance detected.
Link (V7 -1) -?> V6 (19/21):
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Link (V7 -2) -?> V6 (20/21):
Subset 0: () gives pval = 0.48406 / val = 0.291
Non-significance detected.
Link (V7 -3) -?> V6 (21/21):
Subset 0: () gives pval = 0.81090 / val = -0.102
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Algorithm converged for variable V6
## Variable V7
Iterating through pc_alpha = [0.05]:
# pc_alpha = 0.05 (1/1):
Testing condition sets of dimension 0:
Link (V1 -1) -?> V7 (1/21):
Subset 0: () gives pval = 0.10602 / val = 0.613
Non-significance detected.
Link (V1 -2) -?> V7 (2/21):
Subset 0: () gives pval = 0.13143 / val = -0.580
Non-significance detected.
Link (V1 -3) -?> V7 (3/21):
Subset 0: () gives pval = 0.20399 / val = -0.503
Non-significance detected.
Link (V2 -1) -?> V7 (4/21):
Subset 0: () gives pval = 0.31711 / val = 0.407
Non-significance detected.
Link (V2 -2) -?> V7 (5/21):
Subset 0: () gives pval = 0.40496 / val = 0.343
Non-significance detected.
Link (V2 -3) -?> V7 (6/21):
Subset 0: () gives pval = 0.49089 / val = -0.287
Non-significance detected.
Link (V3 -1) -?> V7 (7/21):
Subset 0: () gives pval = 0.92032 / val = 0.043
Non-significance detected.
Link (V3 -2) -?> V7 (8/21):
Subset 0: () gives pval = 0.79775 / val = -0.109
Non-significance detected.
Link (V3 -3) -?> V7 (9/21):
Subset 0: () gives pval = 0.75377 / val = 0.133
Non-significance detected.
Link (V4 -1) -?> V7 (10/21):
Subset 0: () gives pval = 0.75703 / val = -0.131
Non-significance detected.
Link (V4 -2) -?> V7 (11/21):
Subset 0: () gives pval = 0.07150 / val = -0.666
Non-significance detected.
Link (V4 -3) -?> V7 (12/21):
Subset 0: () gives pval = 0.87683 / val = 0.066
Non-significance detected.
Link (V5 -1) -?> V7 (13/21):
Subset 0: () gives pval = 0.97094 / val = 0.016
Non-significance detected.
Link (V5 -2) -?> V7 (14/21):
Subset 0: () gives pval = 0.62396 / val = -0.206
Non-significance detected.
Link (V5 -3) -?> V7 (15/21):
Subset 0: () gives pval = 0.16865 / val = 0.538
Non-significance detected.
Link (V6 -1) -?> V7 (16/21):
Subset 0: () gives pval = 0.98554 / val = -0.008
Non-significance detected.
Link (V6 -2) -?> V7 (17/21):
Subset 0: () gives pval = 0.90824 / val = -0.049
Non-significance detected.
Link (V6 -3) -?> V7 (18/21):
Subset 0: () gives pval = 0.13870 / val = 0.572
Non-significance detected.
Link (V7 -1) -?> V7 (19/21):
Subset 0: () gives pval = 0.50733 / val = 0.277
Non-significance detected.
Link (V7 -2) -?> V7 (20/21):
Subset 0: () gives pval = 0.93834 / val = 0.033
Non-significance detected.
Link (V7 -3) -?> V7 (21/21):
Subset 0: () gives pval = 0.92994 / val = -0.037
Non-significance detected.
Sorting parents in decreasing order with
weight(i-tau->j) = min_{iterations} |val_{ij}(tau)|
Updating parents:
Variable V7 has 0 link(s):
Algorithm converged for variable V7
## Resulting lagged parent (super)sets:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): max_pval = 0.00058, |min_val| = 0.938
Variable V3 has 0 link(s):
Variable V4 has 1 link(s):
(V3 -2): max_pval = 0.02698, |min_val| = 0.765
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): max_pval = 0.00000, |min_val| = 0.992
Variable V7 has 0 link(s):
##
## Step 2: PC algorithm with contemp. conditions and MCI tests
##
Parameters:
independence test = par_corr
tau_min = 0
tau_max = 3
pc_alpha = 0.05
contemp_collider_rule = majority
conflict_resolution = True
reset_lagged_links = False
max_conds_dim = None
max_conds_py = None
max_conds_px = None
max_conds_px_lagged = None
fdr_method = none
--------------------------
Skeleton discovery phase
--------------------------
Testing contemporaneous condition sets of dimension 0:
Link (V1 0) o?o V2 (1/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V2 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.78838 / val = 0.126
Non-significance detected.
Link (V1 0) o?o V3 (2/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.96748 / val = 0.017
Non-significance detected.
Link (V1 0) o?o V4 (3/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V3 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.27373 / val = 0.482
Non-significance detected.
Link (V1 0) o?o V5 (4/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.89723 / val = 0.055
Non-significance detected.
Link (V1 0) o?o V6 (5/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.46578 / val = -0.333
Non-significance detected.
Link (V1 0) o?o V7 (6/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32813 / val = 0.399
Non-significance detected.
Link (V2 0) o?o V1 (7/45):
Already removed.
Link (V2 -2) -?> V2 (8/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -4) ]
Subset 0: () gives pval = 0.00773 / val = -0.887
No conditions of dimension 0 left.
Link (V2 0) o?o V3 (9/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.11874 / val = -0.644
Non-significance detected.
Link (V2 0) o?o V4 (10/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V3 -2) ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.95232 / val = 0.032
Non-significance detected.
Link (V2 0) o?o V5 (11/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.33073 / val = 0.434
Non-significance detected.
Link (V2 0) o?o V6 (12/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.49710 / val = 0.349
Non-significance detected.
Link (V2 0) o?o V7 (13/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V2 -2) ]
Subset 0: () gives pval = 0.93791 / val = -0.037
Non-significance detected.
Link (V3 0) o?o V1 (14/45):
Already removed.
Link (V3 0) o?o V2 (15/45):
Already removed.
Link (V3 0) o?o V4 (16/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V3 -2) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.42232 / val = 0.364
Non-significance detected.
Link (V3 -2) -?> V4 (17/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.02698 / val = -0.765
No conditions of dimension 0 left.
Link (V3 0) o?o V5 (18/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.95447 / val = 0.024
Non-significance detected.
Link (V3 0) o?o V6 (19/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.53674 / val = -0.284
Non-significance detected.
Link (V3 0) o?o V7 (20/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.25153 / val = -0.460
Non-significance detected.
Link (V4 0) o?o V1 (21/45):
Already removed.
Link (V4 0) o?o V2 (22/45):
Already removed.
Link (V4 0) o?o V3 (23/45):
Already removed.
Link (V4 0) o?o V5 (24/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V3 -2) ]
Subset 0: () gives pval = 0.16356 / val = 0.590
Non-significance detected.
Link (V4 0) o?o V6 (25/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ (V3 -2) ]
Subset 0: () gives pval = 0.84717 / val = -0.102
Non-significance detected.
Link (V4 0) o?o V7 (26/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V3 -2) ]
Subset 0: () gives pval = 0.68274 / val = -0.190
Non-significance detected.
Link (V5 0) o?o V1 (27/45):
Already removed.
Link (V5 0) o?o V2 (28/45):
Already removed.
Link (V5 0) o?o V3 (29/45):
Already removed.
Link (V5 0) o?o V4 (30/45):
Already removed.
Link (V5 0) o?o V6 (31/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ (V7 -1) ]
with conds_x = [ ]
Subset 0: () gives pval = 0.38468 / val = 0.392
Non-significance detected.
Link (V5 0) o?o V7 (32/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.32066 / val = -0.404
Non-significance detected.
Link (V6 0) o?o V1 (33/45):
Already removed.
Link (V6 0) o?o V2 (34/45):
Already removed.
Link (V6 0) o?o V3 (35/45):
Already removed.
Link (V6 0) o?o V4 (36/45):
Already removed.
Link (V6 0) o?o V5 (37/45):
Already removed.
Link (V6 0) o?o V7 (38/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ (V7 -1) ]
Subset 0: () gives pval = 0.09642 / val = -0.675
Non-significance detected.
Link (V7 0) o?o V1 (39/45):
Already removed.
Link (V7 0) o?o V2 (40/45):
Already removed.
Link (V7 0) o?o V3 (41/45):
Already removed.
Link (V7 0) o?o V4 (42/45):
Already removed.
Link (V7 0) o?o V5 (43/45):
Already removed.
Link (V7 0) o?o V6 (44/45):
Already removed.
Link (V7 -1) -?> V6 (45/45):
Iterate through 1 subset(s) of conditions:
with conds_y = [ ]
with conds_x = [ ]
Subset 0: () gives pval = 0.00000 / val = 0.992
No conditions of dimension 0 left.
Updated contemp. adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 0 link(s):
Variable V3 has 0 link(s):
Variable V4 has 0 link(s):
Variable V5 has 0 link(s):
Variable V6 has 0 link(s):
Variable V7 has 0 link(s):
Algorithm converged at p = 0.
----------------------------
Collider orientation phase
----------------------------
contemp_collider_rule = majority
conflict_resolution = True
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2)
Variable V3 has 0 link(s):
Variable V4 has 1 link(s):
(V3 -2)
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
----------------------------
Rule orientation phase
----------------------------
Try rule(s) [1 2 3]
Updated adjacencies:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2)
Variable V3 has 0 link(s):
Variable V4 has 1 link(s):
(V3 -2)
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1)
Variable V7 has 0 link(s):
## Significant links at alpha = 0.05:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): pval = 0.00773 | val = -0.887
Variable V3 has 0 link(s):
Variable V4 has 1 link(s):
(V3 -2): pval = 0.02698 | val = -0.765
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): pval = 0.00000 | val = 0.992
Variable V7 has 0 link(s):
##
## Scores for individual pc_alpha values:
pc_alpha = 0.001 yields score = 14.18332
pc_alpha = 0.005 yields score = 14.18332
pc_alpha = 0.01 yields score = 12.05241
pc_alpha = 0.025 yields score = 12.05241
pc_alpha = 0.05 yields score = 11.33224
##
## Results for optimal pc_alpha = 0.05
##
## Significant links at alpha = 0.05:
Variable V1 has 0 link(s):
Variable V2 has 1 link(s):
(V2 -2): pval = 0.00773 | val = -0.887
Variable V3 has 0 link(s):
Variable V4 has 1 link(s):
(V3 -2): pval = 0.02698 | val = -0.765
Variable V5 has 0 link(s):
Variable V6 has 1 link(s):
(V7 -1): pval = 0.00000 | val = 0.992
Variable V7 has 0 link(s):
[16]:
from dowhy.utils.timeseries import create_graph_from_networkx_array
graph = create_graph_from_networkx_array(results['graph'], var_names)
plot(graph)
