Log-linear analysis is a technique used in statistics to examine the relationship between more than two categorical variables.
(A Pearson's chi-square test could be used instead of log-linear analysis, but that technique only allows for two of the variables to be compared at a time.
that has an approximate chi-square distribution when the sample size is large:[2] where There are three assumptions in log-linear analysis:[2] 1.
[1] The goal of log-linear analysis is to determine which model components are necessary to retain in order to best account for the data.
This results in the likelihood ratio chi-square statistic being equal to 0, which is the best model fit.
Backward elimination is used to determine which of the model components are necessary to retain in order to best account for the data.
Specifically, at each stage, after the removal of the highest ordered interaction, the likelihood ratio chi-square statistic is computed to measure how well the model is fitting the data.
The highest ordered interactions are no longer removed when the likelihood ratio chi-square statistic becomes significant.
Else, if the chi-square difference is larger than the critical value, the less parsimonious model is preferred.
[1] Once the model of best fit is determined, the highest-order interaction is examined by conducting chi-square analyses at different levels of one of the variables.
To conduct chi-square analyses, one needs to break the model down into a 2 × 2 or 2 × 1 contingency table.
[2] For example, if one is examining the relationship among four variables, and the model of best fit contained one of the three-way interactions, one would examine its simple two-way interactions at different levels of the third variable.
To compare effect sizes of the interactions between the variables, odds ratios are used.
Odds ratios are preferred over chi-square statistics for two main reasons:[1] 1.