The data in "injury.txt" have binary columns corresponding to sex, location, and seat belt use. The remaining columns are for the type of injury, coded i1 to i5.

injury = read.table(file.choose(), header=TRUE) # injury.txt

sex location seatbelt i1 i2 i3 i4 i5 f urban no 7287 175 720 91 10 f urban yes 11587 126 577 48 8 f rural no 3246 73 710 159 31 f rural yes 6134 94 564 82 17 m urban no 10381 136 566 96 14 m urban yes 10969 83 259 37 1 m rural no 6123 141 710 188 45 m rural yes 6693 74 353 74 12

(a) 3ptsState the additive (no interactions) model that relates the odds of each injury category, versus i5 as the baseline, as a function of sex, location, and seat belt use. Define any symbols that you use.

(b) 5ptsCan any of these predictor terms be removed? Explain your reasoning (you may use = 0.05 for any significance level thresholds), and report the final model.

(c) 3ptsIf alternatively these injury categories were treated as ordinal with numeric values 1, 2, 3, 4, and 5 representing increasing severity, state the proportional-odds, cumulative logit model for response category j. Define any symbolsif not already defined in part (a).

(d) 4ptsIs the proportional odds assumption reasonable for this data set? Carry out an appropriate test. State the hypotheses in terms of the model notation you used in part (c) above, and state the conclusion using = 0.05