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Analysis of categorical data by linear models. (English) Zbl 1149.62317
Summary: Assume there are \(n_i\) \((i=1,2,\cdots,s)\) samples from \(s\) multinomial distributions, each having \(r\) categories of response. Then define any \(u\) functions of the unknown true cell probabilities \(\{\pi_{ij}: i=1,2,\cdots,s; j=1,2,\cdots,r\), where \(\sum_{i=1}^r\pi_{ij}=1\}\) that have derivatives of order up to the second with respect to \(\pi_{ij}\) and for which the matrix of first derivatives is of rank \(u\).
A general noniterative procedure is described for fitting these functions to a linear model, for testing the goodness-of-fit of the model, and for testing hypotheses about the parameters in the linear model.
The special cases of linear functions and logarithmic functions of the \(\pi_{ij}\) are developed in detail, and some examples of how the general approach can be used to analyze various types of categorical data are presented.

62J05 Linear regression; mixed models
62G10 Nonparametric hypothesis testing
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