In http://yetanothermathprogrammingconsultant.blogspot.nl/2015/02/logistic-regression.html we implemented a simple maximum likelihood problem which replicates the results from R on a medium size data set (n=400 cases). The question is of course: why can’t we use some least squares objective. The answer is: this problem turns out to be a non-convex problem and thus we may get into trouble.
The can look like:
Of course if you like, we can substitute out the r’s and obtain an unconstrained problem. Note that x and y are data.
Some solvers can solve this, but others have some issues:
|Conopt, Ipopt, Knitro|| |
|Minos, Snopt|| |
**** ERRORS/WARNINGS IN EQUATION fit(id1)
Indeed the maximum likelihood version of the model seems easier to solve.