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Bayesian sampling‐based approach for factor analysis models with continuous and polytomous data
Author(s) -
Shi JianQing,
Lee SikYum
Publication year - 1998
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1998.tb00679.x
Subject(s) - polytomous rasch model , gibbs sampling , bayesian probability , generalization , latent variable , econometrics , computer science , statistics , posterior probability , factor analysis , mathematics , data mining , item response theory , psychometrics , mathematical analysis
Factor analysis is an important technique in behavioural science research in explaining the interdependence and assessing causations and correlations of the observed variables and the latent factors. Recently, generalization of the model to handle polytomous variables has received a lot of attention. In this paper, a Bayesian approach to analysing the model with continuous and polytomous variables is developed. In the posterior analysis, the observed continuous and polytomous data are augmented with the latent factor scores and the unobserved measurements underlying the polytomous variables. Random observations from the posterior distributions are simulated via the Gibbs sampler algorithm. It is shown that the conditional distributions involved in the implementation of the algorithm are the familiar distributions, hence the simulation is rather straightforward. Joint Bayesian estimates of the unknown thresholds, structural parameters and the factor scores are produced simultaneously. The efficiency and accuracy of our approach are demonstrated by a real‐life example and a simulation study.