To give some background I am working to replicate a study using R where a multinomial conditional logit model was used to estimate the likelihood a college football recruit would attend a specific university. The general problem statement can be found here:
The equation presented in the paper is based on the idea a recruit (j) of position (k) receives utility (or disutility) from factors associated with a particular university (z).
In broad strokes the model and application of the conditional mlogit model make sense - it takes into account both characteristics specific to the choice and the individual. However, when I began to attempt the solution using R and the mlogit package I was confused about the classification of variables. A description of the mlogit package by Yves Croissant classifies 3 types of variables:
When I went to see what this looked like it practice - it ended up creating the individual specific variables with alternative specific coefficients and alternative specific variables with alternative specific coefficients by making interaction terms. For example, if an individual with an income variable was choosing a mode of travel it would interact income with travel mode.
This seemed like a red flag because the results of the college choice paper presented general coefficients that were not tied to a specific player/college interaction. My current hunch is that although the equation presented made it appear as if they used individual and alternative specific variables in practice they just treated everything using generic coefficients?
My overall question is - how do I go about choosing the variable types for this problem? Does anyone have any helpful resources or walkthroughs with example data sets where a conditional mlogit model is applied to a data set? In particular, an example where the choice-set is not constant across all individuals (on average each recruit chooses between 6 schools and these schools vary a lot between recruits)? Is a multinomial logit model even the correct approach (there seems to be some fuzziness in the naming conventions of these types of models)?