Keunggulan Pendugaan Model Aditif dengan Pendekatan Model Linear Campuran Dibanding dengan Algoritma Backfitting

Abstract

The additive model is the generalized of multiple linear regression that expresses the mean of a reponse variable as a sum of functional form of predictors. The widely used estimation of additive models described in Hastie and Tibshirani (1990) is backfitting algorithm. However, the algorithm with linear smoothers gave some difficulties when it comes to model selection and its inference. The additive model with P-spline as smooth function admits a mixed model formulation, in which variance components control the non-linearity degree in the smooth function. This research is focused in comparing of estimation additive models using backfitting algorithm and linear mixed model approach. The research results show that estimation of additive models using linear mixed models offer simplicity in the computation, since use low-rank dimension of P-spline, and in the model inference, since based on maximum likelihood method. Estimation additive model using linear mixed model approach can be suggested as an alternative method beside backfitting algorithm