Mixed-effects location and scale Tobit joint models for heterogeneous longitudinal data with skewness, detection limits, and measurement errors

Abstract

The joint modeling of mean and variance for longitudinal data is an active research area. This type of model has the advantage of accounting for heteroscedasticity commonly observed in between and within subject variations. Most of researches focus on improving the estimating efficiency but ignore many data features frequently encountered in practice. In this article, we develop a mixed-effects location scale joint model that concurrently accounts for longitudinal data with multiple features. Specifically, our joint model handles heterogeneity, skewness, limit of detection, measurement errors in covariates which are typically observed in the collection of longitudinal data from many studies. We employ a Bayesian approach for making inference on the joint model. The proposed model and method are applied to an AIDS study. Simulation studies are performed to assess the performance of the proposed method. Alternative models under different conditions are compared.

A Latent Variable Mixed-Effects Location Scale Model with an Application to Daily Diary Data

“…A mixed-effects location scale model extends the more common applications of latent curve and mixed-effects models to uniquely address heterogeneity of variance both in the random effects at the second level and the within-subject residuals. Some advancements of this framework have included extensions to bivariate versions of the model to study multiple longitudinal variables, including dyad data involving distinguishable individuals (Pugach et al 2014 ), a 3-level model (Lin et al 2018 ), and joint models to handle combinations of response distributions (Lu 2017 ). Most applications have relied on ML estimation, but Bayesian estimation of these models is an alternative (Lin et al).…”

Co-Occurrence of Metal Contaminants in United States Public Water Systems in 2013–2015

“…Tobit regression models account for censored data [18][19][20][21] and mixed-effect Tobit models further account for clustering of observations in a dataset [21]. Mixed-effect Tobit regression models of the log-transformed contaminants, left-censored at the logtransformed MRL, with normally distributed random intercepts for public water system and state, but no fixed effects, were used to predict the mean log-concentrations of each contaminant for each public water system.…”

Catching Up on Multilevel Modeling

“…However, MELSMs are more broadly applicable, such as for ordinal outcomes (Hedeker et al, 2016), time-to-event and censored outcomes (Courvoisier et al, 2019;Lu, 2018), and semicontinuous outcomes (i.e., with excess zeros; Blozis et al, 2020) or random effects (Ma et al, 2021). MELSMs have also been extended to dyadic data (Rast & Ferrer, 2018), cross-classified designs (Brunton-Smith et al, 2017), three-level designs (Li & Hedeker, 2012;Lin et al, 2018), and to include nonlinear fixed effects (Bürkner, 2018;Williams et al, 2019).…”