Log-linear models for cross-tabulations using Stata

Log-linear models for cross-tabulations are models for describing and testing patterns in cross-tabulations. These cross-tabulations could have two dimensions (e.g. father’s occupation versus son’s occupation) or more than two dimensions (e.g. father’s occupation versus son’s occupation for different cohorts and different countries). A wide range of patterns can be investigated and tested with these models. Some examples of these patterns are: one can investigate whether the dimensions are independent (e.g. father’s occupation has no relevance for the son’s occupation), whether the dimensions are independent except for the diagonals (e.g. sons are more likely to enter the occupation of their father, but the father has no influence once the son chooses to do something else than the father) or assume that the categories are ordinal and estimate a scale for each dimension and summarize the strength of the association with one number, which can be compared across cohorts or countries. The purpose of this talk is to give an overview of this family of models, discuss how to trick Stata (in particular, poisson and gsem) into estimating these models, and how to get interpretable parameters out of these models.