A C(,P) METHOD TO SELECT A LOG LINEAR MODE

Categorical data in contingency tables are collected in many investigations. In order to understand and identify the type of structures in such tables appropriate log linear models are fit. Existing model selection methods assume that the weighted error variance is unity based on an underlying probability distribution that is either multinomial, Poisson or product multinomial. However, due to the sampling design the above underlying distributions may not hold. As a result the weighted error variance may not be unity and therefore interactions may appear significant even when they are not.;There is a need to identify the important effects. One way to do this is to estimate the variance from the provided data and then to incorporate it in a method of model building.;This research develops a C(,p) criterion that may be used to compare log linear models fitted to a given dataset whether or not the error variance is unity. We describe how to obtain an estimate of the weighted error variance for use by the C(,p) criterion. Since there are many log linear models when the number of variables defining a contingency table is four or more, we propose methods of identifying important interactions so that many fewer models (compared to fitting all possible models) need to be evaluated in order to find the model that minimizes the C(,p) criterion.;Adjusted R('2).;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;is also proposed here as another criterion that is capable of comparing all possible models.;A simulation study is conducted to compare various methods of model selection and to investigate methods to estimate the variance. In it interactions are defined with varying noncentrality parameters. The methods are compared using a risk statistic (minimum mean square error). The results of the simulation study indicate the following: The model chosen by the C(,p) method contains the interactions that should be included in the log linear model for given data. The.;(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI).;on the other hand, includes too many interactions in the chosen model and hence is a poor method for model selection. The standard methods, the methods of Goodman (Technometrics, 1971), Brown (Applied Statistics, 1976) and Wermuth (Biometrics, 1976), all assume that the weighted error variance for log linear model is unity. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI.