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 $3p$ 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.

This study investigates the geographically weighted multivariate logistic regression (GWMLR) model, parameter estimation, and hypothesis testing procedures. The GWMLR model is an extension to the multivariate logistic regression (MLR) model, which has dependent variables that follow a multinomial distribution along with parameters associated with the spatial weighting at each location in the study area. The parameter estimation was done using the maximum likelihood estimation and Newton-Raphson methods, and the maximum likelihood ratio test was used for hypothesis testing of the parameters. The performance of the GWMLR model was evaluated using a real dataset and it was found to perform better than the MLR model.

In this study, the hypothesis testing of geographically weighted bivariate logistic regression (GWBLR) procedure is proposed. The GWBLR model is a bivariate logistic regression (BLR) model which all of the regression parameters depend on the geographical location in the study area. The geographical location is expressed as a point coordinate in two-dimensional geographic space (longitude and latitude). The response variables of BLR model are constructed from a (2 × 2) contingency table and it follows the multinomial distribution. The purpose of this study is to test the GWBLR model parameters. There are three hypothesis tests. The first is a parameters similarity test using the Vuong test method. The test is to obtain a significant difference between GWBLR and BLR. The second is a simultaneous test using the likelihood ratio test method. The simultaneous test is to obtain the simultaneous significance of the regression parameters. The last is a partial test using Wald test method. The result showed that the Vuong statistic and Wald statistic have an asymptotic standard normal distribution, whereas the likelihood ratio statistic has an asymptotic chi-squared distribution.

Poisson regression is commonly used in modeling count data in various research fields. An essential assumption must be met when using Poisson regression, which is that the count data of the response has the mean and variance must be equal, namely equi-dispersion. This assumption is often unmet because many data for the response that the variance is greater than the mean, called over-dispersion. If the Poisson regression model contains the over-dispersion, then will be produced an invalid model can under-estimate standard errors and misleading inference for regression parameters. Therefore, an approach is needed to overcome the over-dispersion problem in Poisson regression. The generalized Poisson regression can handle the over-dispersion in Poisson regression. This study aims to obtain the generalized Poisson regression model and the factors affecting the low birth weight in Indonesia in 2021. The result shows that the factors affecting the low birth weight in Indonesia based on the generalized Poisson regression model were: poverty rate, percentage of households with access to appropriate sanitation, percentage of pregnant women at risk of chronic energy deficiency receiving additional food, percentage of pregnant women who received blood-boosting tablets, and percentage of antenatal care.

Multinomial Logistics Regression (MLR) is a regression model developed from the Binary Logistics Regression (BLR) model. The response variable of the RLM model has three or more categories and has a multinomial distribution, with the data scale being nominal. The response variable in this study is a combination of the Public Health Development Index (PHDI) status and the Human Development Index (HDI) status of districts/cities in Kalimantan Island, 2018, divided into four categories with category one as a comparison. The predictor variables used were the number of the public health center, the percentage of poor people, economic growth, the pure junior high school participation rate, and the percentage of the population with a minimum of junior high school education. The MLR parameter model was estimated using the Maximum Likelihood Estimation (MLE) method and Newton-Raphson iteration. The hypothesis testing of the MLR model was used by the Likelihood Ratio Test (LRT) method and the Wald test. The best model selection in this study uses the backward method, and the interpretation of the best MLR model uses the odds ratio value. The results showed that the best MLR model is a model that has three predictor variables. The factors that significantly influenced the combination of PHDI status and the HDI status of districts/cities in Kalimantan Island in 2018 were the percentage of poor people, economic growth, and the percentage of people with the minimum level of education in junior high school.

Data mining is essential for decision-makers to analyze and extract insights from data efficiently. Classification is one of the data mining techniques used to organize data based on its features, helping to identify patterns and make predictions. This study evaluates Binary Logistic Regression (BLR), a type of generalized linear model that suitable for binary outcomes, for classifying poverty depth across Indonesian regencies/cities in 2022, with a focus on the impact of different K values in K-Fold Cross Validation. The dataset includes 514 regencies/cities, with the Poverty Depth Index as the target variable, categorized into high (1) and low (0) levels, using 11 predictor variables. K-Fold Cross Validation was performed with K values of 3, 5, and 10, using accuracy and Area Under Curve (AUC) as evaluation metrics. The mean accuracy values for BLR are 75.7% for K=3, 74.3% for K=5, and 75.1% for K=10. Results show that K=3 offers the highest accuracy in classifying poverty depth in Indonesia, with the lowest standard deviation of 0.03. However, K=10 demonstrates superior discriminative ability in BLR, reflected by a higher AUC value. This study highlights the significant influence of K values in K-Fold Cross Validation on BLR performance.