Another look at statistical inference with machine learning-derived data

This repository contains the code and results for the paper "SAnother look at statistical inference with machine learning-imputed data" by Jessica Gronsbell, Jianhui Gao, Zachary R. McCaw, Yaqi Shi, and David Cheng. You can find the preprint here.

Overview

The repository includes:

• Implementation of the PB inference methods discussed in the paper, including the CC, PPI, and PDC methods.
• Code for the simulation studies.

Repository Structure

Within the Scripts folder:

• method_functions.R: Contains functions for the PB inference methods methods

Within each of the Simulation Studies sub-folders:

• run_sim.R: Script for running simulations
• simple_data_generation.R: Contains functions for data generation
• plotting_functions.R: Contains functions for plotting
• simulation_results.Rmd: Markdown to replicate the simulation studies

[Note: Additional R packages are required for plotting and parallelization in the markdown file.]

Within the Data folder:

• example_data.csv: Simple data to run the example at the end of this README file.

Requirements

Install the following R packages before running an analysis.

install.packages(c("dplyr", "tidyr", "lmtest", "sandwich"))

Example

Below is a simple demonstration of how to run an analysis.

# Load analysis functions.
source('method_functions.R')

# Read in example data for linear regression.
analysis_data <- read.csv('example_data.csv', row.names = 1)

# Quick peak at the data.
head(analysis_data)

# Specify the model formula and GLM family.
formula <- y - pred ~ x1 + x2 + x3 + x4 + x5 
family <- "gaussian"

# Run the analysis. 
analysis_results <- rbind(
  classical_estimation(analysis_data, formula, family, est_type = "classical"),
  pb_estimation(analysis_data, formula, family, est_type = "ppi"),
  pb_estimation(analysis_data, formula, family, est_type = "chen-chen"),
  pb_estimation(analysis_data, formula, family, est_type = "pdc"))

You will obtain the following output.

# Review results for coefficient for x1. 
analysis_results %>% filter(term == "x1")
# A tibble: 4 × 6
  Estimate Std.Error Lower.CI Upper.CI Method    term 
*    <dbl>     <dbl>    <dbl>    <dbl> <chr>     <chr>
1   -0.170    0.0324   -0.233  -0.106  classical x1   
2   -0.169    0.0318   -0.231  -0.107  ppi       x1   
3   -0.169    0.0275   -0.223  -0.115  chen-chen x1   
4   -0.148    0.0301   -0.207  -0.0888 pdc       x1   

Contact

For questions, please contact Jesse Gronsbell or open an issue on this repository.