In this paper, we propose efficient Bayesian methods to analyze longitudinal ordinal data with missing values using multivariate probit models. Longitudinal ordinal data with substantial missing values are ubiquitous in many scientific fields. Specifically, we develop the Markov chain Monte Carlo (MCMC) sampling methods based on the non-identifiable multivariate probit models and further compare their performance with the one based on the identifiable multivariate probit models. We carried out our investigation through simulation studies, which show that the proposed methods can handle substantial missing values and the method with marginalizing the redundant parameters based on the non-identifiable model outperforms the others in the mixing and convergences of the MCMC sampling components. We then present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE).
{"title":"Bayesian Analysis of Longitudinal Ordinal Data with Missing Values Using Multivariate Probit Models.","authors":"Xiao Zhang","doi":"10.18576/jsap/140302","DOIUrl":"https://doi.org/10.18576/jsap/140302","url":null,"abstract":"<p><p>In this paper, we propose efficient Bayesian methods to analyze longitudinal ordinal data with missing values using multivariate probit models. Longitudinal ordinal data with substantial missing values are ubiquitous in many scientific fields. Specifically, we develop the Markov chain Monte Carlo (MCMC) sampling methods based on the non-identifiable multivariate probit models and further compare their performance with the one based on the identifiable multivariate probit models. We carried out our investigation through simulation studies, which show that the proposed methods can handle substantial missing values and the method with marginalizing the redundant parameters based on the non-identifiable model outperforms the others in the mixing and convergences of the MCMC sampling components. We then present an application using data from the Russia Longitudinal Monitoring Survey-Higher School of Economics (RLMS-HSE).</p>","PeriodicalId":37070,"journal":{"name":"Journal of Statistics Applications and Probability","volume":"14 3","pages":"337-352"},"PeriodicalIF":0.0,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12381765/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144972671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Models, mathematical or stochastic, which move from one functional form to another through pathway parameters, so that in between stages can be captured, are examined in this article. Models which move from generalized type-1 beta family to type-2 beta family, to generalized gamma family to generalized Mittag-Leffler family to Lévy distributions are examined here. It is known that one can likely find an approximate model for the data at hand whether the data are coming from biological, physical, engineering, social sciences or other areas. Different families of functions are connected through the pathway parameters and hence one will find a suitable member from within one of the families or in between stages of two families. Graphs are provided to show the movement of the different models showing thicker tails, thinner tails, right tail cut off etc.
{"title":"A Pathway Idea for Model Building.","authors":"A M Mathai, Panagis Moschopoulos","doi":"10.12785/jsap/010102","DOIUrl":"https://doi.org/10.12785/jsap/010102","url":null,"abstract":"<p><p>Models, mathematical or stochastic, which move from one functional form to another through pathway parameters, so that in between stages can be captured, are examined in this article. Models which move from generalized type-1 beta family to type-2 beta family, to generalized gamma family to generalized Mittag-Leffler family to Lévy distributions are examined here. It is known that one can likely find an approximate model for the data at hand whether the data are coming from biological, physical, engineering, social sciences or other areas. Different families of functions are connected through the pathway parameters and hence one will find a suitable member from within one of the families or in between stages of two families. Graphs are provided to show the movement of the different models showing thicker tails, thinner tails, right tail cut off etc.</p>","PeriodicalId":37070,"journal":{"name":"Journal of Statistics Applications and Probability","volume":"1 1","pages":"15-20"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4038346/pdf/nihms442823.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32385049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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