ABSTRACT
Log-linear analysis is a technique for both exploratory and confirmatory analysis of variable relations when all the variables of interest are classification (i.e., categorical) variables. Researchers who are familiar with contingency-table analysis will recognize log-linear analysis as a tool for assessing higher-order relations among two or more classification variables that cannot be achieved with traditional two-variable chi-square analysis. The term log-linear refers to the use of the logarithms of frequencies to create linear models that parallel the linear modeling in analysis of variance (see Chapter 1, this volume). In analysis of variance the mean of the response variable, measured on a quantitative scale, is viewed as a function of effects of explanatory classification variables. For log-linear analysis, it is actually the log of expected frequencies that is associated with factors in a specified explanatory model. Rather than effects, the explanatory variables are the classification variables of interest, so that the test of the model is one of structural relations, rather than effect. A special case of log-linear analysis, logistic regression (see Chapter 16, this volume), has a more direct parallel to analysis of variance, in that there are established response and explanatory variables, as well as a linear function of effects to explain the response. Log-linear analysis involves testing of hypotheses about the interaction among variables of interest. Results provide an understanding of relations and partial relations among these variables. Computations for log-linear analysis can be performed using most major statistical software packages, such as S-Plus, SAS, and SPSS, although the level of user input required varies among the packages. Default settings in software subroutines often do not address hypotheses of interest, so that software use might require a relatively high level of user sophistication. We recommend texts by Agresti (1990), Christensen (1997), and Fienberg (1980). Specific desiderata for applied studies that include log-linear analysis are presented in Table 17.1 and explained in the following sections.
