Estimation Approaches for Generalized Linear Factor Analysis Models with Sparse Indicators

Substance use research involves a number of methodological challenges that require advanced data analysis techniques. Generalized linear factor analysis (GLFA) is a general latent variable modeling framework useful for substance use research that can be applied to continuous or categorical measures. Unfortunately, substance use data is characterized by a large proportion of zeros (sparseness), and sparse endorsement can cause maximum likelihood estimation of GLFA models to fail. However the extent of estimation problems caused by sparseness has not previously been well studied. Because of the great need to improve reliability for estimating models with items with low endorsement, in this study I evaluated Bayesian estimation as an alternative to maximum likelihood estimation for GLFA models with sparse, categorical indicators. I found that the use of priors in Bayesian estimation eliminated extreme parameter estimates, improved estimate efficiency, increased empirical power to detect true effects, and provided meaningful results when models do not converge using ML estimation. I also found that the gains in efficiency and empirical power using Bayesian estimation depend on specifying adequately concentrated priors (i.e. adequate information to constrain inferences), and the increased overall efficiency and empirical power were also tied to a trade-off with overall unbiasedness. In sum, my proposal to use Bayesian estimation with prior information to estimate GLFA models with sparse indicators provides a much needed alternative for substance use researchers who wish to make inferences with sparse data.