In a previous post I have discussed the differences between logistic regression and discriminant function analysis, but how about log-linear analysis? Which, and when, to choose between chi-square, logistic regression, and log-linear analysis?
Lets briefly review each of these statistical procedures: The chi-square test (χ²) is a descriptive statistic, just as correlation is descriptive of the association between two variables. Chi-square is not a modeling technique, so in the absence of a dependent (outcome) variable, there is no prediction of either a value (such as in ordinary regression) or a group membership (such as in logistic regression or discriminant function analysis).
Both logistic regression and log-linear analysis (hypothesis testing and model building) are modeling techniques so both have a dependent variable (outcome) being predicted by the independent variables (predictors). Logistic regression is best for a combination of continuous and categorical predictors with a categorical outcome variable, while log-linear is preferred when all variables are categorical (because log-linear is merely an extension of the chi-square test).
So when deciding between chi-square (descriptive) or logistic regression / log- linear analysis (predictive), the choice is clear: Do you want to describe the strength of a relationship or do you want to model the determinants of, and predict the likelihood of an outcome? Depending on the nature of your variables, the choice is clear.