Predicting a Distal Outcome Variable From a Latent Growth Model: ML versus Bayesian Estimation

Abstract

Latent growth models (LGMs) with a distal outcome allow researchers to assess longer-term patterns, and to detect the need to start a (preventive) treatment or intervention in an early stage. The aim of the current simulation study is to examine the performance of an LGM with a continuous distal outcome under maximum likelihood (ML) and Bayesian estimation with default and informative priors, under varying sample sizes, effect sizes and slope variance values. We conclude that caution is needed when predicting a distal outcome from an LGM when the: (1) sample size is small; and (2) amount of variation around the latent slope is small, even with a large sample size. We recommend against the use of ML and Bayesian estimation with Mplus default priors in these situations to avoid severely biased estimates. Recommendations for substantive researchers working with LGMs with distal outcomes are provided based on the simulation results.

Comparing Hyperprior Distributions to Estimate Variance Components for Interrater Reliability Coefficients

“…The estimation difficulties in conditions with few raters and low variability are consistent with several studies on the performance of MCMC estimation for hierarchical models (Gelman and Hill 2006;McNeish and Stapleton 2016;Polson and Scott 2012;Smid et al 2019). In the MCMC approach to estimating the ICCs, priors should be specified for the distribution of random effects.…”

“…The choice among hyperprior distributions for random-effect variances is frequently discussed (see e.g., Gelman 2006;Gelman et al 2013;Smid et al 2019;Van Erp et al 2019). Prior and hyperprior distributions can be classified into informative or uninformative distributions, proper or improper distributions, and default, thoughtful or data-dependent distributions.…”

“…Prior and hyperprior distributions can be classified into informative or uninformative distributions, proper or improper distributions, and default, thoughtful or data-dependent distributions. For more information on these classifications, we refer to Gelman (2006), Gelman et al (2013, chapter 2), and Smid et al (2019).…”

“…Because the variance of these random effects is itself estimated, a prior distribution should be specified for that parameter, called a hyperprior distribution (Gelman et al 2013, p. 107-108). The performance (e.g., bias and efficiency) of the parameter estimates depends on the specification of these hyperpriors (Gelman and Hill 2006;Gelman et al 2013;McNeish and Stapleton 2016;Polson and Scott 2012;Smid et al 2019). The specification of hyperpriors thus provides an opportunity to improve the performance of parameter estimates of random effects.…”

Dangers of the Defaults: A Tutorial on the Impact of Default Priors When Using Bayesian SEM With Small Samples

“…Whether a sample is small depends on the complexity of the model that is estimated. One way to express the size of a sample is to look at the ratio between the number of observations and the number of unknown parameters in the model (e.g., Lee and Song, 2004;Smid et al, 2019a). A sample could be considered very small when this ratio is 2, which means there are just two observations for each unknown parameter.…”