Bayesian Model Selection for Longitudinal Count Data

Abstract

We explore the performance of three popular model-selection criteria for generalised linear mixed-effects models (GLMMs) for longitudinal count data (LCD). We focus on evaluating the conditional criteria (given the random effects) versus the marginal criteria (averaging over the random effects) in selecting the appropriate data-generating model. We advocate the use of marginal criteria, since Bayesian statisticians often use the conditional criteria despite previous warnings. We discuss how to compute the marginal criteria for LCD by a replication method and importance sampling algorithm. Besides, we show via simulations to what extent we err when using the conditional criteria instead of the marginal criteria. To promote the usage of the marginal criteria, we developed an R function that computes the marginal criteria for longitudinal models based on samples from the posterior distribution. Finally, we illustrate the advantages of the marginal criteria on a well-known data set of patients who have epilepsy.

Bayesian model selection for multilevel mediation models

“…Additionally, McNeish and Stapleton (2016) suggested that 20 clusters with five or more observations per cluster might be sufficient if the model is estimated with restrictive maximum likelihood. Overall, the marginal criteria outperformed the conditional ones, which is in line with the other results previously obtained in the literature (see Ariyo et al, 2019a, 2019, 2021; Chan & Grant, 2016b; Merkle et al, 2018; Quintero & Lesaffre, 2018).…”

“…However, there is still no consensus about the best criterion for model selection in a Bayesian context. For the distinction between the performance of the marginal against the conditional criteria, other authors have shown that marginal criteria outperform the conditional criteria in most settings for LMMs with some extensions (Ariyo et al, 2019a, 2019) and generalised linear mixed models (GLMMs) (Ariyo et al, 2021; Millar, 2018; Quintero & Lesaffre, 2018). This is also true for an item response model (Li, Qiu, Zhang, & Feng, 2016; Merkle et al, 2018; Millar, 2018).…”

“…For instance, DIC is not invariant to nonlinear transformations of and negative value for can occur in some cases. The major setback of mDIC is computational difficulties since the integral in Equation (10) is generally intractable, notwithstanding, mDIC as been found to show superior performance in most cases (Ariyo & Adeleke, 2021; Ariyo et al, 2019a, 2021; Ariyo, Lesaffre, et al, 2019; Chan & Grant, 2016a; Quintero & Lesaffre, 2018).…”

“…Li & Yu, 2012; Chan & Grant, 2016a; Celeux, Forbes, Robert, & Titterington, 2006) and via simulation studies (see, e.g. Ariyo & Adeleke, 2021; Ariyo, Lesaffre, Verbeke, & Quintero, 2021; Ariyo et al, 2019a, 2019; Chan & Grant, 2016b; Merkle, Furr, & Rabe‐Hesketh, 2018) that the use of the conditional likelihood is questionable. In the theoretical argument, for instance, Li and Yu (2012) proved that the conditional likelihood of the augmented data is nonregular and disprove the standard asymptotic arguments that are needed to justify the DIC.…”

“…Likewise, Chan and Grant (2016a) show that the numerical SE s of the conditional DICs are often too large to be useful for models' comparison. On practical grounds (Ariyo & Adeleke, 2021; Ariyo et al, 2019a, 2019, 2021; Chan & Grant, 2016b; Merkle et al, 2018; Millar, 2009) provide simulation studies in which the conditional DIC almost always favors an overfitted model.…”