The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Abstract

Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

Empirical performance of estimation methods in Beta mixed models with application to ecological data

“…The most used form of the model (Equation 6) in simulation study is the random intercept model (Hernandez et al, 2014;Hernandez and Giampaoli, 2018) with the following notation:…”

“…The random effect b j has zero mean and variance σ 2 . The fixed effects were set from previous studies (Bauer and Sterba, 2011;Hernandez et al, 2014;Ali et al, 2016;Hernandez and Giampaoli, 2018):…”

“…The variances of the random effect b j were set at σ 2 =0.4, 0.5, 1.1, 2, 3.4. Variances greater than 3.4 were not considered because they caused larger values of the random intercept (Hernandez and Giampaoli, 2018).…”

“…One important assumption of Beta mixed models is that random effects must be normally distributed (Hernandez and Giampaoli, 2018). Indeed, for computational convenience, the random effects are assumed to be normally distributed.…”

“…A natural concern is related to the impact of misspecification of the random effects distribution on the estimators used. Previous studies investigating the impact of the misspecification focused on linear, logistic, Poisson and Weibull mixed models (Litière et al, 2008;Hernandez et al, 2014;Hernandez and Giampaoli, 2018). But no significant studies have considered Beta mixed models.…”