Premium
Estimation of factor scores with polytomous data by the EM algorithm
Author(s) -
Shi JianQing,
Lee SikYum
Publication year - 1997
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.2044-8317.1997.tb01142.x
Subject(s) - polytomous rasch model , mathematics , bayesian probability , posterior probability , covariance , covariance matrix , statistics , distribution (mathematics) , factor analysis , algorithm , computer science , item response theory , psychometrics , mathematical analysis
The main objective of this paper is to investigate the application of the EM algorithm for obtaining a Bayesian estimate of the factor score in a factor analysis model with polytomous data. The posterior distribution of the latent factor score given the manifest continuous or polytomous observations is derived, and then the EM algorithm is utilized to find the posterior mode estimate of the distribution. It is shown that both the E‐step and the M‐step of the algorithm are very simple. An expression for the covariance matrix of the posterior distribution is derived. Results of a simulation study are presented to illustrate some properties of the estimate and the EM algorithm.