A comparison of nominal regression and logistic regression for contingency tables, including the 2 × 2 × 2 case in causality

Logistic regression (LR) is one of the most used estimation techniques for nominal data collected in contingency tables, and the question arises how the recently proposed concept of nominal correlation and regression (NCR) relates to it. (1) LR targets the cells in the contingency table while NCR targets only the variables. (2) Where the methods seem to overlap, such as in the 2 × 2 × 2 case, there still is the difference between the use of categories by LR (notably the categories Success, Cause and Confounder) and the use of variables by NCR (notably the variables Effect, Truth and Confounding). (3) Since LR looks for the most parsimonious model, the analysis might be helped by NCR, that is very parsimonious since it uses only the variables and not all the cells of the contingency table. (4) While LR may generate statistically significant regressions, NRC may show that the correlation still is low. (5) Risk difference regression may be a bridge to understand more about the difference between LR and NCR. (6) The use of LR and NCR next to each other may help to focus on the research question and the amount of detail required for it.