Tutz, Gerhard; Leitenstorfer, Florian
Generalized smooth monotonic regression.
Collaborative Research Center 386, Discussion Paper 417
Common approaches to monotonic regression focus on the case of a unidimensional covariate and continuous dependent variable. Here a general approach is proposed that allows for additive and multiplicative structures where one or more variables have monotone influence on the dependent variable. In addition the approach allows for dependent variables from an exponential family, including binary and Poisson distributed dependent variables. Flexibility of the smooth estimate is gained by expanding the unknown function in monotonic basis functions. For the estimation of coefficients and the selection of basis functions a likelihood based boosting algorithm is proposed which is simply to implement. Stopping criteria and inference are based on AIC-type measures. The method is applied to several data sets.