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Abstract:
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The Pearson and likelihood ratio statistics are commonly used to test goodness-of-fit for models applied to count data from a multinomial distribution. When data are from a table formed by the cross-classification of a large number of manifest variables, the common statistics may have low power and inaccurate Type I error level due to sparseness. Several statistics defined on marginal distribution have been proposed to remedy this issue. Some of these statistics, fit to binary cross classified variables, have good performance for Type I error rate and power when the data table is formed from a moderate number of manifest variables. However, when the number of manifest variables becomes larger than 20, these statistics have limitations in terms of computer resources. This paper compares the performance of several Goodness-of-fit statistics for multinomial data when number manifest variables is larger than or equal to 25. The study will also investigate performance of a bootstrap method to obtain p-values for Pearson-Fisher statistic, fit to confirmatory dichotomous variable factor analysis model, when the number of manifest variables is larger than or equal to 25.
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