NCJ Number
85333
Date Published
1981
Length
22 pages
Annotation
The application of log-linear models to contingency tables is explained and illustrated using criminal justice data.
Abstract
Until recently, the statistical tools available for the analysis of categorical data have been crude, but in the past decade a great deal of work has been conducted on the development and application of log-linear models to contingency table problems. The advantage of the log-linear approach to contingency table analysis is in its ability to construct complex linear models, analogous in many respects to the models underlying 'standard' regression analysis. As a result, researchers may go beyond simple tests for marginal independence and instead construct and test detailed models hypothesizing higher-order interactions. Major points noted in the discussion are that (1) in the application of log-linear models, the expected frequencies are calculated prior to estimation of the model parameters (this is directly opposite to the procedure used in the general linear model); (2) instead of using ordinary least squares procedures, iterative proportional fitting techniques are used in generating maximum likelihood estimates of the expected values; and (3) the error terms or residuals of models fit to contingency table data cannot be assumed to be normally distributed, nor can homoscedasticity be assumed, so that measures of goodness-of-fit other than the F ratio must be used, such as the chi-square statistic. The models are applied to a contingency table broken down by age of offender, type of murder, and the sex of the offender. Tabular data and mathematical equations are provided, and 22 references are listed.