Estimasi Probit Biner Semiparametrik Spline Truncated pada Status Persentase Penduduk Miskin

Abstract

Regression analysis is a statistical method used to model the relationship between predictor variables and response variables. To analyse categorical response variables, probit regression can be used. There are three probit models based on the type of response variable, namely binary probit, multinomial probit, and ordinal probit. Binary probit is a method used to analyse response variables with two categories. Probit models are often used because they produce more stable probabilities in small samples because it uses the normal distribution. There are three types of binary probit models based on curve approaches, namely parametric, non-parametric, and semi-parametric. Semi-parametric regression was chosen because it combines parametric and non-parametric components. Conventional semi-parametric regression often cannot provide accurate estimates. Therefore, the use of truncated splines is relevant because they can handle the flexibility of unknown functions. This study aims to estimate a semi-parametric binary probit model with truncated splines using maximum likelihood estimation. The resulting likelihood function is not in closed form, requiring Newton-Raphson numerical iteration. The results show that the best model is obtained with one knot point, which has an accuracy of 84.21% and an AUC of 0.84, indicating that the model's prediction classification is verry good.