Ang. [Gretl-devel] forward selection procedure and foreach loops

I tend to agree with Sven that "forward selection" is not a great thing to add. However, I mentioned that it might be useful for pedagogical purposes. To that end I've written a function that some people might like to experiment with. One gives a base specification for a model, with the unconditionally included regressors in list0, along with a list of possible additional regressors, list1. The function searches list1 for the regressor, x*, which gives the greatest improvement in the AIC. If there is such an x*, it is added to list0 and removed from list1, and the search is repeated. The search stops when no further improvement in AIC is possible, or when list1 is exhausted, whichever comes first. Obviously one could modify the function to use a different criterion for "improvement" at each step, or make it fancier by adding a control parameter to select from a given menu of such criteria (e.g. AIC, BIC, HQC, adjusted R^2). The example below uses Ramanathan's data4-10, and contains a caution, namely a demonstration that the model arrived at via this algorithm does _not_ in fact offer the "best" AIC that can be achieved with the available regressors. Neither of the variables INCOME or COLLEGE individually improves the AIC in relation to the model selected by the forward procedure, but jointly they do. function addlist (series y, list list0, list list1) ols y list0 --quiet aic_min = $aic printf "Baseline AIC = %g\n", aic_min loop while (nelem(list1) > 0) --quiet string bestx = null # check each remaining additional regressor loop foreach i list1 --quiet ols y list0 $i --quiet aic = $aic if (aic < aic_min) aic_min = aic string bestx = "$i" endif endloop if isstring(bestx) printf "Adding %-8s AIC = %g\n", @bestx, aic list list0 += @bestx list list1 -= @bestx else break endif endloop printf "\nMinimized AIC = %g, with this model:\n", aic_min ols y list0 end function open data4-10 list list0 = 0 list list1 = 2 3 4 5 6 7 8 9 addlist(ENROLL, list0, list1) # but compare... ols ENROLL 0 CATHOL WHITE INCOME COLLEGE