I am attempting to model the finishing position (independent variable) of runners in a race based upon height, weight, age, gender, past results (dependent variables). Thusfar I have performed an ordered logit regression from which I can generate predicted probabilities of a runner finishing in a given position. However, the probabilities of all runnings coming first do not sum to one, nor do sum of the probabilities of a runner finishing in any position. So I'm not sure how useful these predicted values are. My preferred software package is Stata, but also have R and Matlab. My best attempt thus far is to run
ologit y x1 x2... xn
and then scale down the predicted values so they sum to one, but this seems a bit rough and I suspect the resulting numbers are biased in some way. My question is: How do a perform a conditional ordered logit / probit regression?