Zero-Inflated Poisson Regression Testing In Handling Overdispersion On Poisson Regression - Mutia Sari; Open Darnius (JMEA : Journal of Mathematics Education and Application, 2023)
The classical linear regression analysis is an analysis aimed at knowing the relationship between the response variables and the explanatory variables assuming the normal distribution data, but in the applied data is often not the case. Generalized Linear Model (GLM) was developed for data in the form of categorical and discrete distribution. In this study the data was raised which has a poisson distribution by as much as n, with average  λ and the odds appearing zero p. Poisson regression is GLM for Poisson-distributed data assuming that Var(X ) = E(X ), but asusumption is rare in applied data. For rare occurrences of a specified interval X variables are often zero-valued, thus causing overdispersion (Var(X ) E(X )). Lambert (1992) introduced a method for overcoming overdispersion in poisson regression i.e. the Zero-Inflated Poisson regression (ZIP). In this research conducted a ZIP regression test in overcoming overdispersion to see the opportunity limit p appears zero- valued as the value that causes overdispersion. Testing is done with RStudio ver. 1.1.463.0 software. Based on the simulated data obtained that Regression ZIP stopped overcoming overdis persion at the condition n = 500, λ = 0.7 with the odds p = 0.2 with a dispersion ratio of  τ = 1.010.