Latent Variable Measurement Error Correction with lpmec
Date: 2026-02-05

# Latent Variable Measurement Error Correction with `lpmec`

#### 2026-02-05

## 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"
    )

    ## {booti_ 1 of 11} -- {parti_ 1 of 5}

    ## {booti_ 1 of 11} -- {parti_ 2 of 5}

    ## {booti_ 1 of 11} -- {parti_ 3 of 5}

    ## {booti_ 1 of 11} -- {parti_ 4 of 5}

    ## {booti_ 1 of 11} -- {parti_ 5 of 5}

    ## {booti_ 2 of 11} -- {parti_ 1 of 5}

    ## {booti_ 2 of 11} -- {parti_ 2 of 5}

    ## {booti_ 2 of 11} -- {parti_ 3 of 5}

    ## {booti_ 2 of 11} -- {parti_ 4 of 5}

    ## {booti_ 2 of 11} -- {parti_ 5 of 5}

    ## {booti_ 3 of 11} -- {parti_ 1 of 5}

    ## {booti_ 3 of 11} -- {parti_ 2 of 5}

    ## {booti_ 3 of 11} -- {parti_ 3 of 5}

    ## {booti_ 3 of 11} -- {parti_ 4 of 5}

    ## {booti_ 3 of 11} -- {parti_ 5 of 5}

    ## {booti_ 4 of 11} -- {parti_ 1 of 5}

    ## {booti_ 4 of 11} -- {parti_ 2 of 5}

    ## {booti_ 4 of 11} -- {parti_ 3 of 5}

    ## {booti_ 4 of 11} -- {parti_ 4 of 5}

    ## {booti_ 4 of 11} -- {parti_ 5 of 5}

    ## {booti_ 5 of 11} -- {parti_ 1 of 5}

    ## {booti_ 5 of 11} -- {parti_ 2 of 5}

    ## {booti_ 5 of 11} -- {parti_ 3 of 5}

    ## {booti_ 5 of 11} -- {parti_ 4 of 5}

    ## {booti_ 5 of 11} -- {parti_ 5 of 5}

    ## {booti_ 6 of 11} -- {parti_ 1 of 5}

    ## {booti_ 6 of 11} -- {parti_ 2 of 5}

    ## {booti_ 6 of 11} -- {parti_ 3 of 5}

    ## {booti_ 6 of 11} -- {parti_ 4 of 5}

    ## {booti_ 6 of 11} -- {parti_ 5 of 5}

    ## {booti_ 7 of 11} -- {parti_ 1 of 5}

    ## {booti_ 7 of 11} -- {parti_ 2 of 5}

    ## {booti_ 7 of 11} -- {parti_ 3 of 5}

    ## {booti_ 7 of 11} -- {parti_ 4 of 5}

    ## {booti_ 7 of 11} -- {parti_ 5 of 5}

    ## {booti_ 8 of 11} -- {parti_ 1 of 5}

    ## {booti_ 8 of 11} -- {parti_ 2 of 5}

    ## {booti_ 8 of 11} -- {parti_ 3 of 5}

    ## {booti_ 8 of 11} -- {parti_ 4 of 5}

    ## {booti_ 8 of 11} -- {parti_ 5 of 5}

    ## {booti_ 9 of 11} -- {parti_ 1 of 5}

    ## {booti_ 9 of 11} -- {parti_ 2 of 5}

    ## {booti_ 9 of 11} -- {parti_ 3 of 5}

    ## {booti_ 9 of 11} -- {parti_ 4 of 5}

    ## {booti_ 9 of 11} -- {parti_ 5 of 5}

    ## {booti_ 10 of 11} -- {parti_ 1 of 5}

    ## {booti_ 10 of 11} -- {parti_ 2 of 5}

    ## {booti_ 10 of 11} -- {parti_ 3 of 5}

    ## {booti_ 10 of 11} -- {parti_ 4 of 5}

    ## {booti_ 10 of 11} -- {parti_ 5 of 5}

    ## {booti_ 11 of 11} -- {parti_ 1 of 5}

    ## {booti_ 11 of 11} -- {parti_ 2 of 5}

    ## {booti_ 11 of 11} -- {parti_ 3 of 5}

    ## {booti_ 11 of 11} -- {parti_ 4 of 5}

    ## {booti_ 11 of 11} -- {parti_ 5 of 5}

Compare naive and corrected estimates:

    print(results)

    ## Latent Predictor Measurement Error Correction (LPMEC) Model Results
    ## -------------------------------------------------------------------
    ## Uncorrected Coefficient (OLS): 0.301 (SE: 0.022)
    ## Corrected Coefficient: 0.430 (SE: 0.021)
    ## Bayesian OLS (Outer): NA (SE: NA)
    ## Use summary() for detailed results.

    summary(results)

    ## Latent Predictor Measurement Error Correction (LPMEC) Model Summary
    ## ====================================================================
    ##                       Estimate         SE  CI_Lower  CI_Upper
    ## OLS                  0.3007980 0.02247701 0.2622669 0.3264330
    ## IV                   0.7489984 0.05586817 0.6639255 0.8199316
    ## Corrected IV         0.4300984 0.02124421 0.3943312 0.4606052
    ## Corrected OLS        0.4300984 0.02124421 0.3943312 0.4606052
    ## Bayesian OLS (Outer)        NA         NA        NA        NA
    ## Bayesian OLS (Inner)        NA         NA        NA        NA

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.