Obtain the Hulsey data from the R package smdata or from https://

dl.dropbox.com/u/1857674/SmiMerBook/SmiMerDoc.html. This file includes two other predictors that were not described in the text. The first predictor, effectiveness, contains subjects’ ratings of the importance of treatment effectiveness on treatment choice. The second predictor, invasiveness, contains subjects’ ratings of the importance of treatment invasiveness on treatment choice. Both ratings were made on a Likert scale where 1 represents “extremely unimportant,” and 6 represents “extremely important.” Recall that the response variable, choice, was made on a scale where 1 indicates “extremely likely to choose angioplasty” and 6 indicates “extremely likely to choose bypass.” Use the data to carry out the following.

(a) Fit a cumulative proportional odds model that contains the three predictor variables effectiveness, invasiveness, and cond. Interpret the estimates associated with the three predictors.

(b) For the medical scenario in the experiment, angioplasty is both less effective and less invasive than bypass. Do your estimates from part

(a) mesh with these details?

(c) Compare cumulative proportional odds models that contain various subsets of the three predictors effectiveness, invasiveness, and cond. Which model(s) do you judge to be best, and why?

(d) Carry out tests of the proportional odds assumption for each of the three predictors. Which predictors appear to violate this assumption? (Hint: In VGAM, we can free the proportional odds assumption for individual predictors using family=cumulative(parallel=FALSE ~ x1), where x1 is the predictor for which we wish to free the proportional odds assumption.)

(e) Fit a cumulative model employing partial proportional odds, using the results from (d). Describe how the interpretations have changed, compared to part

(a). (Note that, if you are using Stata, you will need to download gologit2 to do this.)