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# Analysis of Categorical Data by Linear Models

James E. Grizzle, C. Frank Starmer and Gary G. Koch
Biometrics
Vol. 25, No. 3 (Sep., 1969), pp. 489-504
DOI: 10.2307/2528901
Stable URL: http://www.jstor.org/stable/2528901
Page Count: 16
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## Abstract

Assume there are n$_i$., i = 1, 2, ..., 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, ..., s; j = 1, 2, ..., r, where $\sum^r_{j=1}\pi_{ij}$ = 1} that have derivatives up to the second order 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.

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