Using Data-Dependent Priors to Mitigate Small Sample Bias in Latent Growth Models

Abstract

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been widely developed for LGMs, and fully Bayesian methods, while not dependent on asymptotics, can encounter issues because the choice for the factor covariance matrix prior distribution has substantial influence with small samples. This tutorial discusses differences between LGMs and MEMs and demonstrates how data-dependent priors, an established class of methods that blend frequentist and Bayesian paradigms, can be implemented within M plus 7.1 to abate the small sample bias that is prevalent with LGM software while keeping additional programming to the bare minimum.