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