An efficient Fisher-scoring algorithm for fitting latent class models with individual covariates

TL;DR

This paper introduces an efficient Fisher-scoring algorithm for fitting latent class models with covariates, ensuring stable convergence and robustness against model misspecification, demonstrated through an educational transmission case study.

Contribution

The paper develops a simple, positive definite information matrix and a line search-based maximization algorithm for latent class models with covariates, improving estimation efficiency and stability.

Findings

Algorithm guarantees non-decreasing log-likelihood at each step

Starting values are less critical for convergence

Application demonstrates practical utility in education transmission analysis

Abstract

For latent class models where the class weights depend on individual covariates, we derive a simple expression for computing the score vector and a convenient hybrid between the observed and the expected information matrices which is always positive defnite. These ingredients, combined with a maximization algorithm based on line search, provides an efficient tool for maximum likelihood estimation. In particular, the proposed algorithm is such that the log-likelihood never decreases from one step to the next and the choice of starting values is not crucial for reaching a local maximum. We show how the same algorithm may be used for numerical investigation of the effect of model mispecifications. An application to education transmission is used as an illustration.