ANALISIS REGRESI COUNT DATA UNTUK PEMODELAN JUMLAH KASUS PENYAKIT TUBERKULOSIS DI KABUPATEN BANYUMAS

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. Banyumas Regency is one of the districts with quite high Tuberculosis cases in Central Java. This study aims to analyze the factors that affect the number of tuberculosis cases in Banyumas Regency using regression analysis of count data. Poisson regression is the simplest count data regression model that has the assumption of equidispersion, that is, the mean value equal to the variance. However, in its application, these assumption is often not fulfilled, for example, there are cases of overdispersion (variance value is greater than the mean). In this study, to overcome the case of overdispersion, an approach was used using Generalized Poisson Regression (GPR) and negative binomial regression. The results showed that the data on the number of tuberculosis cases in Banyumas Regency in 2019 was overdispersion. The data modeling of the number of tuberculosis cases in Banyumas Regency with the negative binomial regression model is better than the GPR model. Meanwhile, the only predictor variable that affects the number of tuberculosis cases in Banyumas Regency is the sex ratio of productive age (15-49 years).

Count Regression Models for Analyzing Crime Rates in The East Java Province

Crime rate is the number of reported crimes divided by total population. Several factors could contribute the variability of crime rates among areas. This study aims to model the relationship between crime rates among regencies and cities in the East Java Province (Indonesia) and some potentially explanatory variables based on Statistics Indonesia publication in 2020. The crime rate in the East Java Province was consistently at the top three after DKI Jakarta and North Sumatra during 2017 to 2019. Therefore, it is interesting for us to study further about the crime rate in the East Java. Our preliminary analysis indicates that there is an overdispersion in our sample data. To overcome the overdispersion, we fit Generalized Poisson and Negative Binomial regression. The ratio of deviance and degree of freedom based on Negative Binomial is slightly smaller (1.38) than Generalized Poisson (1.99). The results indicate that Negative Binomial and Generalized Poisson regression, compared to standard Poisson regression, are relatively fit to model our crime rate data. Some factors which contribute significantly (α=0.05) for the crime rate in the East Java Province under Negative Binomial as well as Generalized Poisson regression are percentage of poor people, number of households, unemployment rate, and percentage of expenditure.

Predictors of laxative use in inpatients with schizophrenia on clozapine

Objectives: Constipation, a clinical manifestation of gastrointestinal hypomotility, is a common and potentially serious complication of clozapine therapy, requiring laxatives for its prevention and treatment. We explored the predictive factors of the increased laxative use in inpatients receiving a long-term clozapine therapy. Methods: In the cross-sectional study of 93 patients in a psychiatric rehabilitation hospital, we examined a four-week prevalence of laxative use and a range of demographic and clinical factors associated with the number of prescribed laxatives. Results: Seventy-four percent of inpatients with schizophrenia were prescribed laxatives, and they were statistically significant older and taking higher daily doses of clozapine. In generalized Poisson regression analysis, the clozapine dose, age, and comorbid diabetes mellitus and hypothyroidism were independently associated with the number of concurrently used laxatives. No association was found between the laxatives and gender, duration of clozapine treatment, and the number of other medications with a potential to cause constipation. Conclusion: The clozapine dose, age, diabetes mellitus, and hypothyroidism were shown to be the independent predictors of the increased laxative use among inpatients on clozapine and might be associated with the increased risk of clozapine-induced constipation and gastrointestinal hypomotility.

Estimation and Hypothesis Testing for the Parameters of Multivariate Zero Inflated Generalized Poisson Regression Model

We propose a multivariate regression model called Multivariate Zero Inflated Generalized Poisson Regression (MZIGPR) type II. This model further develops the Bivariate Zero Inflated Generalized Poisson Regression (BZIGPR) type II. This study aims to develop parameter estimation, test statistics, and hypothesis testing, both simultaneously and partially, for significant parameters of the MZIGPR model. The steps of the EM algorithm for obtaining the parameter estimator are also described in this article. We use Berndt–Hall–Hall–Hausman (BHHH) numerical iteration to optimize the EM algorithm. Simultaneous testing is carried out using the maximum likelihood ratio test (MLRT) and the Wald test to partially assess the hypothesis. The proposed MZIGPR model is then used to model the three response variables: the number of maternal childbirth deaths, the number of postpartum maternal deaths, and the number of stillbirths with four predictors. The units of observation are the sub-districts of the Pekalongan Residency, Indonesia. The indicate overdispersion in the data on the number of maternal childbirth deaths and stillbirths, and underdispersion in the data on the number of postpartum maternal deaths. The empirical studies show that the three response variables are significantly affected by all the predictor variables.

Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate generalized Poisson regression

Poisson regression is used to model the data with the response variable in the form of count data. This modeling must meet the equidispersion assumption. That is, the average value is the same as the variance. However, this assumption is often violated. Violation of the equidispersion assumption in Poisson regression modeling will result in invalid conclusions. These violations are an overdispersion and an underdispersion of the response variable. Generalized Poisson Regression (GPR) is an alternative if there is a violation of the equidispersion assumption. If there are two correlated response variables, modeling will use the Bivariate Generalized Poisson Regression (BGPR). However, in the panel data with the observation unit in the form of an area, BGPR is not quite right because there is spatial and temporal heterogeneity in the data. Geographically and Temporally Weighted Bivariate Generalized Poisson Regression (GTWBGPR) is a method for modeling spatial and temporal heterogeneity data. GTWBGPR is a development of GWBGPR. In GTWBGPR, besides accommodating spatial effects, it also accommodates temporal effects. This research will discuss the parameter estimation and test statistics for the GTWBGPR model. Parameter estimation uses Maximum Likelihood Estimation (MLE), but the result is not closed-form, so it is solved by numerical iteration. The numerical iteration used is Newton-Raphson. The test statistic for simultaneous testing uses the Maximum Likelihood Ratio Test (MLRT). With large samples, then this test statistic has a chi-square distribution approximation. So the test statistic for the partial test uses the Z test statistic.

PEMODELAN GEOGRAPHICALLY WEIGHTED GENERALIZED POISSON REGRESSION (GWGPR) PADA KASUS KEMATIAN IBU NIFAS DI JAWA TENGAH

Maternal mortality is one indicator to describing prosperity in a country and indicator of women's health. Most of the maternal mortality caused by postpartum maternal mortality. The number of postpastum maternal mortality is events that the probability of the incident is small, where the incident depending on a certain time or in a certain regions with the results of the observation are variable diskrit and between variable independent each other that follows the Poisson distribution, so that the proper statistical method is Poisson regression. However, in Poisson regression model analysis sometimes assumptions can occur violations, where the value of variance is greater than the mean value called overdispersion. Generalized Poisson Regression (GPR) is one model that can be used to handle overdispersion problems. This modeling produces global parameters for all locations (regions), so to overcome this we need a method of statistical modeling with due regard to spatial factors. The analytical method used to determine the factors that influence the number of postpartum maternal mortality in Central Java that have overdispersion and there are spatial factors, is Geographically Weighted Generalized Poisson Regression (GWGPR) using the Maximum Likelihood Estimation method and Adaptive Bisquare weighting. Poisson regression and GPR modeling produces a variable percentage of pregnant women doing K1 which has a significant effect on the number of postpartum maternal mortality, while for GWGPR modeling is divided into four cluster in all regency/city in Central Java based on the same significant variable. From the comparison of AIC values, it was found that the GWGPR model is better for analyzing postpartum maternal mortality in Central Java because it has the smallest AIC value.Keywords: The Number of Postpartum Maternal Mortality, Overdispersion, Generalized Poisson Regression, Spatial, Geograpically Weighted Generalized Poisson Regression, AIC