A computer program for the generalized chi-square analysis of categorical data using weighted least squares (GENCAT)

Abstract

GENCAT is a computer program which implements an extremely general methodology for the analysis of multivariate categorical data. This approach essentially involves the construction of test statistics for hypotheses involving functions of the observed proportions which are directed at the relationships under investigation and the estimation of corresponding model parameters via weighted least squares computations. Any compounded function of the observed proportions which can be formulated as a sequence of the following transformations of the data vector -- linear, logarithmic, exponential, or the addition of a vector of constants -- can be analyzed within this general framework. This algorithm produces minimum modified chi-square statistics which are obtained by partitioning the sums of squares as in ANOVA. The input data can be either: (a) frequencies from a multidimensional contingency table; (b) a vector of functions with its estimated covariance matrix; and (c) raw data in the form of integer-valued variables associated with each subject. The input format is completely flexible for the data as well as for the matrices.