Are Bayesian regularization methods a must for multilevel dynamic latent variables models?

Due to the increased availability of intensive longitudinal data, researchers have been able to specify increasingly complex dynamic latent variable models. However, these models present challenges related to overfitting, hierarchical features, non-linearity, and sample size requirements. There are further limitations to be addressed regarding the finite sample performance of priors, including bias, accuracy, and type I error inflation. Bayesian estimation provides the flexibility to treat these issues simultaneously through the use of regularizing priors. In this paper, we aim to compare several Bayesian regularizing priors (ridge, Bayesian Lasso, adaptive spike-and-slab Lasso, and regularized horseshoe). To achieve this, we introduce a multilevel dynamic latent variable model. We then conduct two simulation studies and a prior sensitivity analysis using empirical data. The results show that the ridge prior is able to provide sparse estimation while avoiding overshrinkage of relevant signals, in comparison to other Bayesian regularization priors. In addition, we find that the Lasso and heavy-tailed regularizing priors do not perform well compared to light-tailed priors for the logistic model. In the context of multilevel dynamic latent variable modeling, it is often attractive to diversify the choice of priors. However, we instead suggest prioritizing the choice of ridge priors without extreme shrinkage, which we show can handle the trade-off between informativeness and generality, compared to other priors with high concentration around zero and/or heavy tails.