Latent Variable Measurement Error Correction with `lpmec`

In lpmec: Measurement Error Analysis and Correction Under Identification Restrictions

Introduction

This tutorial demonstrates how to use the lpmec package for measurement error correction in regression models using latent variable estimation. The package implements bootstrapped analyses to account for measurement error in observed indicators and provides corrected regression coefficients.

Installation

First install the required dependencies and the lpmec package:

# Install lpmec from source (replace with appropriate installation method)
# devtools::install_github("cjerzak/lpmec-software", subdir = "lpmec")

Basic Usage

Data Simulation

Simulate data with a latent predictor and observed binary indicators:

set.seed(123)
n <- 1000  # Number of observations
d <- 10    # Number of observable indicators

# Generate latent variable and observed outcomes
x_true <- rnorm(n)
Yobs <- 0.4 * x_true + rnorm(n, sd = 0.35)

# Generate binary indicators of latent variable
ObservablesMat <- sapply(1:d, function(j) {
  p <- pnorm(0.5 * x_true + rnorm(n, sd = 0.5))
  rbinom(n, 1, p)
})

Running the Analysis

Use lpmec to estimate corrected coefficients:

library(lpmec)

# Run bootstrapped analysis
results <- lpmec(
  Y = Yobs,
  observables = as.data.frame(ObservablesMat),
  n_boot = 10,      # Reduced for demonstration
  n_partition = 5,  # Reduced for demonstration
  estimation_method = "em"
)

Compare naive and corrected estimates:

print(results)
summary(results)

You can visualize the relationship between split-half estimates:

plot(results)

Advanced Features

Using Different Estimation Methods

The package supports multiple estimation approaches:

# Bayesian MCMC estimation (requires Python environment setup)
if(FALSE){
mcmc_results <- lpmec(
  Y = Yobs,
  observables = as.data.frame(ObservablesMat),
  estimation_method = "mcmc",
  conda_env = "lpmec"  # Specify your conda environment
)
}

Conclusion

The lpmec package provides robust measurement error correction through:

• Bootstrapped latent variable estimation
• Multiple correction methods (OLS, IV, Bayesian)
• Flexible estimation backends (EM, MCMC)

Refer to package documentation for advanced configuration options.

lpmec documentation built on Feb. 9, 2026, 5:07 p.m.