Implementation of F. R. Guo, E. Perković (2022). Efficient Least Squares for Estimating Total Effects under Linearity and Causal Sufficiency.

This is a part of my Ph.D. Preliminary Examination at the Department of Statistics at University of Washington.

All simulations were performed in R v4.1.2 using pcalg v2.7.5. Standard graphical libraries are required along with tidyverse and ggplot2.

install.packages("pcalg")
install.packages("igraph")
install.packages("RBGL")
install.packages("tidyverse")
install.packages("ggplot2")
install.packages("latex2exp")
install.packages("ggh4x")
install.packages("optparse")

• Code\bucket_decomposition.R performs partial causal ordering.
• Code\cpdag.R is my own implementation of coverting a DAG into a CPDAG since the clusters owned by the Department of Statistics at UW had issues running pcalg:::dag2cpdag.
• Code\identifiability.R contains implementation of finding ancestors, descendants, directed paths, etc. Most importantly, it checks for the causal effect identifiability condition.
• Code\mle.R computes the G-regression estimator.
• Code\sampler.R samples random DAGs, treatment sets and outcome variable, and data points.

All simulations are seeded. So they should be reproducible.

$ cd Code
$ Rscript run_simulations.R --num_nodes 10 --treatment_size 2 --n 1000 --num_reps 5 --output ../Results/test.rds

The above command uses the true CPDAG to estimate causal effects. To replicate results in Appendix G where the CPDAG is estimated using Greedy Equivalence Search, replace run_simulations.R with run_simulations_unknown_cpdag.R.

Arguments:

• --num_nodes - Number of nodes in the DAG
• --treatment_size - Number of variables in the treatment set
• --n - Number of iid data points
• --num_reps - Number of replications
• --output - File to store output

The cluster jobs in Code\Slurm\synthetic_sims\ can automate replicating results in the report. The cluster jobs in Code\Slurm\synthetic_sims_ges\ can help replicate results in Appendix G. Plots are generated using Code\results.R. You might need to modify filenamse to accomodate your results.

The dataset was obtained from https://www.synapse.org/#!Synapse:syn3049712/wiki/74630. This is locally available in the Data\ directory. Table 3 in the report can be generated using the following commands:

$ cd Code
$ Rscript dream4_results.R
$ Rscript dream4_bootstrap.R

dream4_results.R generates the normalized squared errors. dream4_bootstrap.R computes standard errors using a bootstrap approach described in Appendix E.