A Logit Model for Bivariate Binary Responses

Abstract

This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

Multilevel bivariate analysis of the association between high-risk fertility behaviors of birth and stunting with associated risk factors in Ethiopia

“…The null hypothesis : = can be tested for independence in the presence of covariates between the two binary outcome variables and ( 40 , 41 ).…”

“…To obtain the parameters estimator of the model, the maximum likelihood method was applied using the Newton–Raphson algorithm iterative procedure. The maximum likelihood estimator can be obtained by determining the first partial derivatives of the log-likelihood function and then equating them to zero ( 41 , 44 ).…”

“…Multilevel bivariate binary logit models are one of the families of multivariate logit models and are used to model the relationships between two correlated binary responses with one or more covariates by considering covariates measured at various levels of a hierarchical structure that affect the outcome variable and how the interactions among covariates measured at different levels affect the outcome variable (39)(40)(41)(42)(43).…”

RELATIONSHIP BETWEEN MSMEs AND FINANCIAL INSTITUTIONS IN WEST ACEH

“…The analysis model used is logistic regression. Logistic regression is a part of the regression analysis that is used when the dependent (response) variable is a dichotomous variable (Purhadi & Fathurahman, 2021).…”

A Comparison of Bivariate Zero-Inflated Poisson Inverse Gaussian Regression Models with and without Exposure Variables

“…Poisson regression requires the assumption that the mean and variance of the response variables must be equal (equidispersion), i.e., one parameter gives both the mean and variance of the distribution. In reality, this assumption may not hold, either with a variance larger than the mean (overdispersion) or otherwise (underdispersion) [1][2][3][4][5]. Such a violation can result in errors in decision making in hypothesis testing due to the occurrence of underestimates [6][7][8].…”