Bayesian Latent Variable Models for Clustered Mixed Outcomes

Abstract

A general framework is proposed for modelling clustered mixed outcomes. A mixture of generalized linear models is used to describe the joint distribution of a set of underlying variables, and an arbitrary function relates the underlying variables to the observed outcomes. The model accommodates multilevel data structures, general covariate effects and distinct link functions and error distributions for each underlying variable. Within the framework proposed, novel models are developed for clustered multiple binary, unordered categorical and joint discrete and continuous outcomes. A Markov chain Monte Carlo sampling algorithm is described for estimating the posterior distributions of the parameters and latent variables. Because of the¯exibility of the modelling framework and estimation procedure, extensions to ordered categorical outcomes and more complex data structures are straightforward. The methods are illustrated by using data from a reproductive toxicity study.

Firm Sustainability Performance Index Modeling

“…The advantages of a Bayesian approach include allowing the use of genuine prior information in addition to that available in the observed data and providing useful statistics, such as mean and percentiles, of the posterior distribution. In addition, as pointed out by many articles in Bayesian analysis of SEM [46][47][48], the sampling based Markov chain Monte Carlo (MCMC) methods do not rely on asymptotic theory and, hence, give more reliable results for situations with small samples. Bayesian estimates of the unknown parameters are obtained from a sufficiently large number of observations, which are sampled from the posterior distribution by the standard Gibbs sampler [49], and the Metropolis Hastings (MH) algorithm [50,51].…”

“…In Bayesian approaches estimation, Dunson [46], Scheines, Hoijtink [47], and Lee and Song [48] believes that this technique allows the researchers to use of genuine prior information in addition to the information that is available in the observed data for producing better outputs, delivers valuable statistics, and indices, such as the mean and percentiles of the posterior distribution of the unknown parameters, and gives more reliable results for small samples. Our study, CSEM and BSEM with cross-sectional data, is able to analyze the impact of knowledge management, business strategy, and organizational learning on firm sustainability performance.…”

Semiparametric latent variable transformation models for multiple mixed outcomes

“…For example, the related literature has focused primarily on joint models for binary and continuous outcomes in a joint normal framework (Catalano and Ryan, 1992;Cox and Wermuth, 1992;Fitzmaurice and Laird, 1995;Sammel et al, 1997;Regan and Catalano, 1999;Dunson, 2000;Roy and Lin, 2000;and Gueorguieva and Agresti, 2001;Song et al, 2009), and in a generalized linear model setting (GLLVM, Moustaki, 1996;Sammel, Ryan, and Legler, 1997;Bartholomew and Knott, 1999;Moustaki and Knott, 2000;Dunson, 2003;Huber et al, 2004;Zhu, Eickhoff and Yan, 2005).…”

Bayesian Modelling and Inference on Mixtures of Distributions

“…Since 2000 alone, they have been adopted in mixture hazard models (Louzada-Neto et al 2002), spatio-temporal models (Stroud et al 2001), structural equation models (Zhu and Lee 2001), disease mapping (Green and Richardson 2002), analysis of proportions (Brooks 2001), correlated data and clustered models (Chib and Hamilton 2000, Dunson 2000, Chen and Dey 2000, classification and discrimination (Wruck et al 2001), experimental design and analysis (Nobile andGreen 2000, Sebastiani andWynn 2000), random effects generalised linear models (Lenk and DeSarbo 2000) and binary data (Basu and Mukhopadhyay 2000). Mixtures of Weibulls (Tsionas 2002) and Gammas (Wiper et al 2001) have been considered, along with computational issues associated with MCMC methods (Liang and Wong 2001), issues of convergence (Liang and Wong 2001), the display…”