Log-linear analysis is a multidimensional extension of the classical cross-tabulation chi-square test. While the latter can maximally consider only two variables at a time, log-linear models can determine complex interactions in multidimensional contingency tables with more than two categorical variables. Indeed, log-linear models combine characteristics of cross-tabulation chi-square tests (determining the fit between observed and expected cell counts) with those of analysis of variance (ANOVA; simultaneous testing of main effects and interactions within multifactorial designs), which is why they are sometimes informally referred to as ANOVA for categorical data. Instead of the Pearson chi-square statistic, log-linear models make use of the likelihood ratio chi-square statistic, which is calculated differently, but has approximately the same distribution when numbers of observations are large. In this ...
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