Parameter Estimation of Zero Inflated Bivariate Ordered Probit Model with Berndt, Hall, Hall, and Hausman Iteration Approach

Andriano Andriano; Purhadi; Ismaini Zain

doi:10.20956/j.v22i1.45316

Authors

Andriano Andriano Department of Statistics, Matana University
Purhadi Department of Statistics, Institut Teknologi Sepuluh Nopember
Ismaini Zain Department of Statistics, Institut Teknologi Sepuluh Nopember

DOI:

https://doi.org/10.20956/j.v22i1.45316

Keywords:

ZIBOPR, MLE, BHHH

Abstract

Probit regression is a statistical analysis method used to analyze the relationship between response variables and predictor variables where the response variable is categorical with a normal distribution link function. Based on the measurement scale, probit regression is divided into two, namely binary probit regression and ordinal probit regression. Based on the number of response variables, ordinal probit regression is divided into two, namely univariate ordinal probit regression and multivariate ordinal probit regression. Multivariate ordinal probit regression that has two response variables is called bivariate ordinal probit regression. In univariate ordinal regression, if there are many unequal proportions in certain categories, conventional univariate probit ordinal regression cannot provide good estimation results. Therefore, univariate ordinal probit regression must be developed into Zero Inflated Ordered Probit (ZIOP) Regression. Similar to univariate ordinal probit regression, bivariate ordinal probit regression produces poor estimates if the response variable is zero inflated, so it is developed into Zero Inflated Bivariate Ordered Probit Regression (ZIBOPR). This study aims to estimate the parameters of the ZIBOPR model, using the Maximum Likelihood Estimator (MLE) method with Brendt, Hall, Hall, and Hausman (BHHH) numerical iteration. This study produces a parameter estimator of the ZIBOPR model, which is a combination of binary probit regression and bivariate ordinal probit regression with the BHHH numerical iteration approach.

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