I need some help in correctly interpreting the results of two regressions calculated for the same data.
The data consists out of several individuals rating multiple classes on n categories like this:
UID | Class | cat_a | cat_b | cat_c | cat_target 1 | A | 0 | 1 | 0 | 1 1 | B | 0 | 1 | 1 | 0 2 | A | 1 | 0 | 0 | 1 2 | B | 0 | 0 | 0 | 0
All rating data is on a scale of 0/1.
My goal was to calculate a shapley-value regression with categories a-c as predictors of dependent variable cat_target.
However I have two ways of doing this:
Run a regression on the individual case data (considering any unique combination of uid and class a case)
Run a regression with the grouped class data (calculating the average category rating for each class), since I have enough classes this is feasible
The results of both regressions differ strongly in the following regards:
- Adjusted r² is much higher for the grouped regression (~.7 vs .07)
- Estimated coefficients and lmg-values differ (e.g. suggesting that cat_a has more predictive value on an individual vs. grouped level)
How can I interpret this correctly? My current intuition would be that they are simply reflecting two different questions:
Can I predict the rating of cat_target an individual will give based on their answers for cat_a-c? (reg 1)
Can I predict the total rating of cat_target for any class based on the total ratings of that class for cat_a-c?
However I have a feeling I am overlooking something and maybe there is even more to it?