A Robust Fit for Generalized Partial Linear Partial Additive Models

In this talk, we propose a robust model fitting algorithm for Generalized Partial Linear Partial Additive Models (GAPLMs), which is a hybrid of the widely-used Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs). The traditional model fitting algorithms are mainly based on likelihood. However, those fits can be severely distorted by the presence of a small portion of atypical observations (also known as "outliers"), which deviate from the assumed model. As a result, the fits become close to those outliers making them not seem atypical. In order to solve this problem, we developed a model fitting algorithm which is resistant to the effect of outliers. To fit the "partial linear partial additive" styled model, our method involves backfitting algorithm and generalized Speckman estimator. To achieve a robust fit, we applied the robust weights derived from robust quasi-likelihood equations proposed by Cantoni and Ronchetti 2001, instead of the likelihood based weights, in generalized local scoring algorithm. To compare the our model fitting performance with the non-robust fit given by the R function gam::gam(), we operated a simulation study and applied the two fitting methods on an example of real dataset. It has been shown in our studies that our robust model fitting algorithm can effectively resist the effect of atypical observations and identify outliers by comparing the robust fitted values with the observed response variable.