Bayesian analysis of multivariate ordered probit model with individual heterogeneity
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Bayesian analysis of multivariate ordered probit model with individual heterogeneity Lei Shi1 Received: 5 April 2019 / Accepted: 14 May 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In recent years, models incorporating heterogeneity among individuals have become increasingly popular in the analyses on subjective ordered choice data. However, there are rare previous studies that include individual heterogeneity in the multivariate ordered probit model. In this article, we describe the Bayesian multivariate ordered probit model introduced by Chen and Dey (in: Dey, Ghosh, Mallick (eds) Generalized linear models: a Bayesian perspective. Marcel-Dekker, New York, pp 133–157, 2000) (Algorithm 1), and propose a new algorithm that includes individual heterogeneity in the cutpoint function (Algorithm 2). Further, we examine the two algorithms using real data from World Values Survey wave 5, collected between 2005 and 2009. The empirical results demonstrate that the model with individual heterogeneity outperforms that without heterogeneity. Keywords Bayesian analysis · Markov chain Monte Carlo (MCMC) · Multivariate ordered probit model · Individual heterogeneity · World values survey JEL Classification C11 · I31
1 Introduction In the research field concerning subjective well-being, outcomes are often arranged ordinally. The ordered probit model is a useful approach to estimate models with this type of data. According to frequentists, an ordered probit model can be estimated
The work was supported by my supervisor Hikaru Hasegawa. Electronic supplementary material The online version of this article (https://doi.org/10.1007/s1018 2-020-00369-2) contains supplementary material, which is available to authorized users. * Lei Shi [email protected] 1
Graduate School of Economics and Business, Hokkaido University, Sapporo, Japan
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using the maximum likelihood method. However, with the development of computer science and the Markov chain Monte Carlo (MCMC) method, Bayesian estimation of the ordered probit model has also become popular. Compared with the non-Bayesian approach to the ordered probit model, the Bayesian approach has several merits. First, as described in Hasegawa and Ueda (2016, p. 359), while the Bayesian method allows the estimation of the multivariate ordered probit model with correlation between explained variables, it is difficult to apply the non-Bayesian approach when the number of explained variables is greater than two.1 Second, the representation of latent variables is particularly useful in the estimation of ordered probit models. The values of the latent variables can easily be obtained from the posterior distribution of the Bayesian sampling algorithm. Following Jeliazkov et al. (2008), there are three main algorithms for the Bayesian analysis of the ordered probit model. The seminal study is Albert and Chib (1993), where the authors proposed a Bayesian sampling algorithm in the univariate ordered probit model. They employed the la
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