Varying-intercept, varying-slope logistic regression: continuing with the speeddating example from the previous exercise, you will now fit some models that allow the coefficients for attractiveness,...

Varying-intercept, varying-slope logistic regression: continuing with the speeddating example from the previous exercise, you will now fit some models that allow the coefficients for attractiveness, compatibility, and the other attributes to vary by person.

(a) Fit a no-pooling model: for each person i, fit a logistic regression to the data yij for the 10 persons j whom he or she rated, using as predictors the 6 ratings r_ij1,...,r_ij6
. (Hint: with 10 data points and 6 predictors, this model is difficult to fit. You will need to simplify it in some way to get reasonable fits.)

(b) Fit a multilevel model, allowing the intercept and the coefficients for the 6 ratings to vary by the rater i.

(c) Compare the inferences from the multilevel model in (b) to the no-pooling model in (a) and the complete-pooling model from part (a) of the previous exercise.