Abstract: In regression analysis, classical linear regression or its transformation methods are not satisfied when response variable is restricted to the interval (0, 1), that is, proportional or fractional data, which is common in Economics, education, medical science etc. One of the most promising approaches is the beta regression proposed by Ferrari and Cribari-Neto. However, the traditional beta regression is confined in the linear situation and thus lacks flexibility. Besides, it has specification error if the true model is not linear. Borrow the idea from generalized additive model (GAM) proposed by Hastie and Tibshirani, a semi-parametric additive beta regression model is proposed. It is assumed the model can be decomposed into parametric and nonparametric parts. For the nonparametric part, the local scoring algorithm is used to fit the unknown function and AIC is used to choose the best smoothing (tuning) parameters. Two simulation examples under different scenarios are conducted, the simulation results shows that semi-parametric beta regression model perform well. Comparing to traditional models, the proposed semi-parametric beta regression model is the best and is significantly better than other traditional models. The proposed model is applied on medical expenditure data to explore the factors of the medical expenditure portion in patients' overall expenditure. It is found marital status, age of householder, income, the number of inpatient and outpatient are the significant factor for the proportion of medical expenditure in overall expenditure.

Key words: semi-parametric, beta regression, generalized additive models, medical expenditure