Independence Analysis of Nominal Data with the Use of Log-Linear Models in R

Log-linear models are used to analyze the relationship between two or more categorical (e.g. nominal or ordinal) variables. The term log-linear derives from the fact that one can, through logarithmic transformations, restate the problem of analyzing multi-way frequency tables in terms that are very similar to ANOVA. Specifically, one may think of the multi-way frequency table to reflect various main effects and interaction effects that add together in a linear fashion to bring about the observed table of frequencies. There are several types of models between dependence and independence: homogenous association, partial association, conditional association and null model. Expected cell frequencies are obtained with the use of iterative proportional fitting algorithm (IPF) [Deming, Stephen 1940]. The next step is to derive model coefficients for single variables as well as for interaction parameter and the most useful tool for interpreting model parameter is odds and odds ratio. Log-linear models are available in R software with the use of loglm function in MASS library and glm function in stats library. In this paper log-linear analysis will be presented with the use of available packages on empirical datasets in economic area.