Why would you use GLM Proc to predict group membership based on a categorical predictor?

Question

Is there a “magic” number of meetings that a student needs to attend in a particular program that has a positive effect on 2nd year retention?

University students, who are at risk of not being retained into the second year, voluntarily participate in one-on-one meetings with a coach throughout their first semester. The program coordinators want to know if there is a magic number of meetings that a student needs to attend in order to be successful (or retained). I think it is really a dosage question. What dose do the students need to get better? So I actually created six groups for the number of meetings.

Group_1 : 2-4 meetings Group_2: 5-7 meetings ….

IV: Categorical (Groups) DV: Dichotomous - Not Retained (0)/Retained (1)

My colleague chose to use the GLM proc in SAS, which I do not know how to use, so I thought I would investigate this is SPSS using the Generalized Linear Model analysis. But it is not clear to me why he used the Generalized Linear Model. When he asked, he said it was a way to compare categorical data. Can someone explain this to me? And how would I do this in SPSS?

Answer 1

If you want to know if there is some particular number of meetings that has a huge effect then I suggest using a regression with a restricted cubic spline of the number of meetings as the independent variable.

If the dependent variable is retained/not retained then this should be a logistic regression which is not in PROC GLM in SAS.

I don't use SPSS though and, in any case, questions about how to do something in particular software packages is off topic here. But look for logistic regression with splines of the IV.

Answer 2

In addition to Peter's advice sometimes for count variables a quadratic fit is good, mainly because it is difficult to choose knot locations in a spline function when there are many tied values.

As said by @DJohnson it is not appropriate to pre-group an ordinal variable as this is making pre-judgements about the dose-response relationship and making the peculiar assumption of piecewise flatness. But I have reservations related to her comment of hoping the buckets were created post hoc. This would create a bias that inflates type I error and hurts confidence interval coverage.