A Bayesian solution to non-convergence of crossed random effects models

When observations (trials) are nested within combinations of subjects and stimuli, crossed random effects models simultaneously take into account both fixed effects and random effects of the subjects and stimuli; however, maximum likelihood estimation (MLE) and restricted maximum likelihood (REML) estimation often encounter convergence problems, which in turn lead to researchers fitting simpler models (e.g., only random intercepts). If the random effect structure is too simple, tests of fixed effects are not valid; if the random effect structure is too complex, tests of fixed effects are inefficient. This study examines issues of estimation, convergence and problems inherent with MLE and REML. We investigated whether Bayesian estimation can solve the convergence problem through a simulation study, which makes a case for adopting a Bayesian approach for estimation, especially when using crossed random effects models. In our simulation study were found that both MLE and REML encountered convergence problems even when trying to fit the correctly specified model and simpler versions of it. Bayesian estimation of models converged 100% of the time, and for the correctly specified model, the parameter estimates were accurate estimates for both fixed and random effects and were essentially unbiased. In sum, the Bayesian approach is a viable alternative to MLE/REML, because models fit by Bayesian estimation solves the non-convergence problem and yields valid and efficient estimates.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Educational Psychology

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2020

Author dc:creator

• Huang, Mingya

Contributors dc:contributor

• Anderson, Carolyn Jane
• Kern, Justin
• Zhang, Jinming

• Crossed-Random Effects Models, convergence, MLE, REML, Bayesian model estimation

Statement dc:rights

• Copyright 2019 Mingya Huang

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/106411

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/106411