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Avoiding boundary estimates in latent class analysis by Bayesian posterior mode estimation. (English) Zbl 1102.62024

Summary: In maximum likelihood estimation of latent class models, it often occurs that one or more of the parameter estimates are on the boundary of the parameter space; that is, that estimated probabilities equal 0 (or 1) or, equivalently, that logit coefficients equal minus (or plus) infinity. This not only causes numerical problems in the computation of the variance-covariance matrix, it also makes the reported confidence intervals and significance tests for the parameters concerned meaningless. Boundary estimates can, however, easily be prevented by the use of prior distributions for the model parameters, yielding a Bayesian procedure called posterior mode or maximum a posteriori estimation. This approach is implemented in, for example, the Latent GOLD Software packages for latent class analysis. Little is, however, known about the quality of posterior mode estimates of the parameters of latent class models, nor about their sensitivity for the choice of the prior distribution.
We compare the quality of various types of posterior mode point and interval estimates for the parameters of latent class models with both the classical maximum likelihood estimates and the bootstrap estimates proposed by L. M. De Menezes [Br. J. Math. Stat. Psychol. 52, 149–168 (1999)]. Our simulation study shows that parameter estimates and standard errors obtained by the Bayesian approach are more reliable than the corresponding parameter estimates and standard errors obtained by maximum likelihood and parametric bootstrapping.

MSC:

62F15 Bayesian inference
62F40 Bootstrap, jackknife and other resampling methods

Software:

Latent GOLD
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