Semiparametric Bivariate Probit Model Using Newton Raphson Approach Early Breastfeeding Initiation and Exclusive Breastfeeding
Suci Amalia, Vita Ratnasari*, Ismaini Zain

Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia
*vita_ratna[at]statistika.its.ac.id

Abstract

Regression analysis in which the response variable is categorical can be processed using the probit model. The probit model is based on the normal distribution, in addition to its interpretation based on marginal effect values. A probit model consisting of two response variables is called the bivariate probit model, in which the response variables each consist of two categories. The predictor variables in bivariate probit model can be either categorical and also continuous data. Bivariate probit model both response variables have a relationship. One of the developments of the bivariate probit model is the semiparametric bivariate probit model, where the bivariate probit model in which there is a parametric and a nonparametric model in this case in the form of a continuous covariate smooth function. Semiparametric bivariate probit model have the advantage of being able to address the problem of nonlinearity of undetected continuous predictor variables that can cause modeling inaccuracies that can effect the results of estimation accuracy. Parameter estimation of semiparametric bivariate probit model uses the Penalized Maximum Likelihood Estimation approach, but the equation obtained is not closed form so iteration are needed to solve it. The iteration used is Newton Raphson. The case study is data on early breastfeeding initiation and exclusive breastfeeding in East Java Province in 2021 obtained from the SUSENAS (National Sosioeconomic Survey) of Badan Pusat Statistik (BPS).

Keywords: Early Breastfeeding Initiation- Exclusive Breastfeeding- Newton Raphson- Penalized Maximum Likelihood Estimation- Semiparametric Bivariate Probit

Topic: Mathematics and Statistics