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A latent class pattern mixture model for nonignorable nonresponses in multivariate categorical data.

Jungwun Lee1, Margaret Lloyd Sieger2, Jon D Phillips3

  • 1Department of Biostatistics, Boston University School of Public Health, 801 Massachusetts Ave, Boston, 02118, MA, United States.

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Summary
This summary is machine-generated.

This study introduces a new model for handling missing survey data, crucial for psychology and education research. It identifies distinct patterns in responses and missing data, improving analytical validity.

Keywords:
Bayesian inferenceEM algorithmLatent class analysisMissing not at randomParental substance use disorder

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Area of Science:

  • Statistics
  • Psychometrics
  • Behavioral Science

Background:

  • Survey data with categorical variables are common in psychology, education, and behavioral studies.
  • Nonignorable missing values in such data can compromise statistical inference validity.
  • Existing methods may not adequately address complex missingness patterns in categorical outcomes.

Purpose of the Study:

  • To propose a novel latent pattern mixture model for analyzing nonignorable missing values in multivariate categorical outcomes.
  • To provide robust statistical methods for handling missing data in complex survey designs.
  • To enhance the validity of inferences drawn from survey research with missing data.

Main Methods:

  • Development of a latent pattern mixture model with two categorical latent variables: one for nonresponse patterns and another for response patterns conditional on nonresponse.
  • Implementation of two parameter estimation strategies: maximum-likelihood (ML) via the expectation-maximization (EM) algorithm and Bayesian estimation using Markov-Chain Monte Carlo (MCMC).
  • Conducting simulation studies to compare the performance of ML and Bayesian estimation methods under varying sample sizes.

Main Results:

  • Simulation studies indicated that maximum-likelihood estimation is generally preferred for large sample sizes due to lower standardized biases.
  • Bayesian estimation with noninformative priors showed advantages in smaller sample sizes.
  • A real data example identified six distinct latent classes characterized by unique response and missingness patterns in a study on parental substance use disorder.

Conclusions:

  • The proposed latent pattern mixture model offers a flexible framework for addressing nonignorable missing data in categorical survey research.
  • Both ML and Bayesian estimation methods are viable, with optimal choice dependent on sample size.
  • The model effectively reveals underlying structures in response and missingness, aiding interpretation in applied research.