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It is shown in this note that for testing discrepancy between a set of observed proportions in k mutually exclusive cells and corresponding expected probabilities, Neyman’s statistic is n / (n – 1) times the Jöreskog and Sörbom chi square goodness-of-fit of a factor model with no latent variables but with mean structures for (k – 1) binary indicators coding for the k-cell category. When the empirical data lead to a rejection of hypothesized model, the modification index gives useful information about post hoc tests for categorical data.
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Daisy et al. (2023) studied this question.