Hierarchical Loglinear Models for Higher Order Cross-Tabs

Abstract

The chi-square test is traditionally used for analyzing two dimensional contingency tables, otherwise called cross-tabs or interaction matrices (Chap. 38). It can answer questions like: is the risk of falling out of bed different between the departments of surgery and internal medicine (Chaps. 37 and 38). The analysis is, however, limited, because only the interaction between the two variables, e.g., (1) falling out of bed (yes, no) and (2) department (one or the other) is assessed. In contrast, in an observational data set we may be interested in the effects of the two variables separately:

• 1. is there a significant difference between the numbers of patients falling out of bed and the patients who don’t (the main effect of variable 1),

• 2. is there a difference between the numbers of patients being in one department and those being in the other (the main effect of variable 2).

The chi-square test is unable to answer such questions. Hierarchical loglinear modeling is a pretty novel methodology adequate for the purpose, but not yet widely available.