A generalization of the difference of slopes test to Poisson regression with three-way interaction

Linear regression models involving interaction can use the difference of slopes test to compare slopes for various situations. We will be generalizing this process to develop a procedure to compare rates in a Poisson regression model, allowing us to consider unbounded count data as opposed to continuous data. We will apply this process to an educational data set from a sample of students located in two different Los Angeles high schools. Our model will include a three-way interaction and address the following questions: (1) Does language ability impact the relationship between math ability and attendance in the same way for males and females? (2) Does gender impact the relationship between math ability and attendance in the same way for students with high language ability versus students with low language ability?...