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On fitting latent class models for binary data: The estimation of standard errors
Author(s) -
Menezes L. M.
Publication year - 1999
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 - 10.1348/000711099159026
Subject(s) - estimator , standard error , asymptotic analysis , parametric statistics , binary data , mathematics , binary number , statistics , parametric model , asymptotic distribution , reliability (semiconductor) , delta method , class (philosophy) , computer science , artificial intelligence , arithmetic , power (physics) , physics , quantum mechanics
We investigate the uncertainty of the estimators in unrestricted latent class analysis applied to binary data. First, we use maximum likelihood theory to obtain asymptotic estimates for the standard errors of the parameters. Second, we consider models that were fitted to data from two large surveys and compare the asymptotic standard errors with empirical estimates obtained using a parametric bootstrap. Third we investigate the variability of the asymptotic standard errors via a simulation study, which gives insights into their reliability. Results show the importance of estimating and reporting standard errors. However, they also indicate serious problems due to very small or very large parameter values, sparse data or sample sizes that are not sufficiently large to enable the estimation of the asymptotic standard errors. Finally, we discuss alternatives designed to handle some of the problems identified in this study, especially circumstances where the parametric bootstrap becomes a useful tool.