Generalized additive models (GAM's) 


Model descriptionSince their introduction by Hastie & Tibshirani in the late 80ies, GAM's have become very popular. This example shows how to fit a GAM using penalized splines. The reason why GAM's can easily be handled in ADMBRE is that penalized splines are a special case of random effects. ADMBRE automatically estimates the degrees of freedom for each spline component, as this only amounts to estimate the variance of the random effects. A more detailed discussion of the model and the estimation approach can be found here: union.pdfThe data, which are available from Statlib (lib.stat.cmu.edu/), contain information for each of 534 workers about whether they are members (y=1) of a workers union or not (y=0). The goal is to model the probability of membership as a function of various covariates. The file union.s shows how to create design matrices for Bsplines in R (SPlus). When sourced into R, union.s creates the input file for ADMB union.dat. You can use it as a basis for you own spline models. If you find the Rfunction gam too restrictive, the following extensions are easily accommodated in ADMBRE:
ResultsThe probability of union membership as function of covariates (with all remaining covariateeffects fixed at their sample means): 