regression analysis for ranking data

[Summer Xavier]

I have got a list of universities ranking with several indices like age, scale, research funding and etc. I want to do a regression analysis between ranking and other indices. Ordered data regression model seems plausible using oprobit or ologit command in Stata. However, order variable in traditional ordered data model usually takes only a few values, for instance, Standard&Poor's ratings. The number of different values of order variable, as you can see in my data set, equals exactly the number of observations whatever how many observations I have. Also, in this type of data set, adding or substracting some samples may alters the value of order variable while in usual ordered data this will not happen. I don't whether it is a good idea to make regression analysis using ordered data model.

[Nick Cox]

An issue with plain regression is the possibility that predicted values are off the scale. In practice I suspect that regressions of any kind with such data will produce low R-square or equivalent and this may not bite. But suppose you have n universities with ranks 1 to n. Then (rank - 0.5) / n falls inside 0 to 1 and you can call up logit or probit with impunity so long as you think about error
structure.

Some writers (e.g. Frank Harrell) are very positive about ordered logit or probit with many, many categories but I suspect that you have to be Frank Harrell to carry that off. Doing it for the first time might be unnerving.

[Summer Xavier]

Thank you very much professor! You really helps me a lot!!