Goodness-of-Fit Testing for Latent Class Models
- 1 July 1993
- journal article
- Published by Taylor & Francis in Multivariate Behavioral Research
- Vol. 28 (3) , 375-389
- https://doi.org/10.1207/s15327906mbr2803_4
Abstract
Latent class models with sparse contingency tables can present problems for model comparison and selection, because under these conditions the distributions of goodness-of-fit indices are often unknown. This causes inaccuracies both in hypothesis testing and in model comparisons based on normed indices. In order to assess the extent of this problem, we carried out a simulation investigating the distributions of the likelihood ratio statistic G2, the Pearson statistic ⊃2, and a new goodness-of-fit index suggested by Read and Cressie (1988). There were substantial deviations between the expectation of the chi-squared distribution and the means of the G2 and Read and Cressie distributions. In general, the mean of the distribution of a statistic was closer to the expectation of the chi-squared distribution when the average cell expectation was large, there were fewer indicator items, and the latent class measurement parameters were less extreme. It was found that the mean of the χ2 distribution is generally c...Keywords
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