Interpreting Three-way Interactions Using SAS

ABSTRACT When factors such as treatment group, sex, or race are in interaction with a continuous variable, testing for homogeneity of slopes is straightforward. However, when there is a significant 3-way interaction between two continuous variables and a categorical variable for analysis of a continuous dependent variable, the interpretations become complex. The next step should be to look at the parameter estimates to look for trends for interpretation purposes but this is a daunting task since the interaction involves multiple continuous values. This paper will present an approach that will dichotomize one of the continuous variables at the median, obtain the parameter estimates of the slopes for the all combinations of categorical variables, and then graphically represent the separate trends across the levels of the continuous variable. The technique is then repeated for the other continuous variable. The method requires assessing two different graphs where the dependent variable is regressed over a different continuous variable in each graph. This has proven to be an easier approach for interpretation and graphically reporting of the outcomes.