Abstract
Regression analysis is an analysis used to model the relationship between the dependent variable (Y) and the independent variable (X). If the dependent variable is a discrete random variable, it is developed using the Poisson regression model. Poisson regression models require non-over-dispersion model assumptions. To deal with over-dispersion, a Generalized Poisson regression model was developed. Generalized Poisson regression (GPR) model is an extension of the Poisson regression model. In this study a GPR model is applied to model the number of dengue hemorrhagic fever (DHF) sufferers in East Nusa Tenggara Province in 2018. The independent variables used include percentage of poor population (X1), population density (X2), percentage of proper sanitation (X3), percentage of decent homes (X4), number of doctors (X5), percentage of access to improved drinking water (X6), average length of schooling (X7), human development index (X8). In the resulting model, Poisson regression experiences multicollinearity and overdisception occurs. To overcome multicollinearity, variable selection is performed. Based on the measurement of the goodness of the model using AIC, the GPR model provides better accuracy than Poisson regression to model DHF in East Nusa Tenggara which is 218.5.
Highlights
Regression analysis is a method used to analyze the relationship between two variables, namely the dependent variable with the independent variable
One regression model that can be used to analyze the relationship between the dependent variable in the form of discrete data with an independent variable is the Poisson regression model
One of the assumptions that must be met in the Poisson regression model is the variance of the dependent variable whose value is equal to the average
Summary
Regression analysis is a method used to analyze the relationship between two variables, namely the dependent variable with the independent variable. One regression model that can be used to analyze the relationship between the dependent variable in the form of discrete data with an independent variable is the Poisson regression model. One of the assumptions that must be met in the Poisson regression model is the variance of the dependent variable whose value is equal to the average. This is in accordance with the characteristics of the Poisson distribution ie the value of variance is the same as the average value. In the analysis of discrete data with Poisson regression models sometimes violations of assumptions can occur, where the variance value is greater than the mean value called overdispersion or the variance is smaller than the mean value called underdispersion.
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