The Impact of Prior Information on Bayesian Latent Basis Growth Model Estimation

Abstract

Latent basis growth modeling is a flexible version of the growth curve modeling, in which it allows the basis coefficients of the model to be freely estimated, and thus the optimal growth trajectories can be determined from the observed data. In this article, Bayesian estimation methods are applied for latent basis growth modeling. Because the latent basis coefficients are important parameters that determine the growth pattern in latent basis growth models, we evaluate the impact of different priors for the basis coefficients on parameter recovery and model estimation. Noninformative priors, informative priors with varying levels of accuracy and precision, and data-dependent priors are considered. In addition, the issue of model specification is treated as a prior selection procedure. The impact of model misspecification and priors for model parameters are investigated simultaneously. A Monte Carlo simulation study is conducted and suggests that misspecified models adversely affect the parameter estimation much more than inaccurate priors. Recommendations on prior selection in latent basis growth models are given based on the simulation results. A real data example on the development of schoolchildren's reading ability is also provided to illustrate the comparison among different sets of priors.

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

“…The results of Bayesian estimation with Mplus default priors (BayesDefault condition) in the current study, are in line with the many recent simulation studies, claiming Bayesian estimation with default priors is not preferred when sample sizes are small (see, e.g., Depaoli & Clifton, 2015;Holtmann, Koch, Lochner, & Eid, 2016;McNeish, 2016aMcNeish, , 2016bShi & Tong, 2017). Spikes were detected when default priors were used in two conditions: (1) when sample sizes were small, and (2) when the slope variance and effect size were small in combination with all examined sample sizes.…”

“…One might therefore opt to choose BayesDefault instead of risking the specification of deviating priors (when comparing BayesDefault to situations when the prior deviates from the population in the current study). However, as discussed earlier, BayesDefault can lead to severely biased estimates when samples are small (see, e.g., Depaoli & Clifton, 2015;Holtmann et al, 2016;McNeish, 2016aMcNeish, , 2016bShi & Tong, 2017), and is therefore hard to recommend as a viable approach.…”

A Bayesian Approach to the Analysis of Local Average Treatment Effect for Missing and Non-normal Data in Causal Modeling: A Tutorial With the ALMOND Package in R

“…If no prior is specified in the function, the model will be estimated with non-informative priors as default. We encourage users to use informative priors or the data dependent priors (i.e., using the maximum likelihood estimates as the hyperparameters) to obtain more reliable parameter estimates (McNeish, 2016;Shi and Tong, 2017a). The default priors in the package are data-dependent priors.…”

Bayesian Estimation of the Prevalence and Test Characteristics (Sensitivity and Specificity) of Two Serological Tests (RB and SAT-EDTA) for the Diagnosis of Bovine Brucellosis in Small and Medium Cattle Holders in Ecuador

“…In practice, accessing prior knowledge made it possible to know estimations of the model parameters. Therefore, prior information should be sought and incorporated in terms of prior distributions [ 46 , 47 ]. Additionally, the large sample size (22,126 animals) made a corrective strategy, which allowed the data “to speak for itself” [ 48 ].…”