A Note on Calculating the π* Index of Fit for the Analysis of Contingency Tables

Abstract

Rudas, Clogg, and Lindsay (1994) proposed a mixture index-of-fit approach for evaluating goodness of fit in the analysis of contingency tables. Clogg, Rudas, and Xi (1995) applied this approach to the analysis of models for mobility tables. The maximum likelihood estimate of the mixture index of fit π* can be obtained by the expectation and maximization (EM) algorithm. The objective of this article is to describe an alternative algorithm, using sequential quadratic programming (SQP). Two major advantages SQP holds over the EM algorithm are the following: (1) The speed of convergence is greatly increased and (2) SQP is more general than the EM algorithm of Rudas et al. and does not require explicit maximum likelihood estimates. The SQP algorithm is available in the MATLAB package; a sample code is provided in the appendix.