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Mixed Model On the Bayesian Zero Inflated Spatio-Temporal for Relative Risk Diagnostic of DHF Incidences

Mukhsar, A. Sani, B. Abapihi, E. Cahyono, R. Raya

Abstract



Bayesian modeling of count data with local characteristics is commonly found in many cases, such as dengue hemorrhagic fever (DHF). The DHF data are is generally containing excess zeros, especially when it is measured as spatial and temporal data. Regression model of Bayesian zero-inflated Poisson spatio-temporal (BZIP S-T) is often used to analyze such data. The BZIP S-T, called the convolution extended (CE) model, has been introduced, but it does not adjust the excess zeros yet. The BZIP S-T structure is the mixing of three main components; spatial heterogeneity, two random effects (locally and globally) and temporal trend. The BZIP S-T is expressed as a generalized linear model because the DHF data is not continuous and skewed. The performance of both models was verified by using DHF data in 10 districts of Kendari-Indonesia for 84 months, the period of 2008-2014, as response variables. Rainfall and population density are as predictors. Markov Chain Monte Carlo (MCMC) method is to estimate the parameters of both models via their full conditional distributions, respectively. Estimation parameters of both models achieve the convergence at 10,000 iterations with 20,000 burn-in. They were confirmed that trace plots are in the same zone (no extreme value), evolutions of ergodic mean are stable in confidence interval, and autocorrelations of plot are sufficient the Markov Chain properties. Both models indicating the rainfall and the population density statistically have a significant impact on dengue cases in Kendari city. The BZIP S-T deviance is smaller than the CE deviance, then the BZIP S-T is the better model. The BZIP S-T investigation shows that Puwatu and Kadia district are consistent as DHF highest locations in Kendari. Both districts are endemic DHF locations.

Keywords


Bayesian spatio-temporal, DHF, excess zeros, generalized linear model, MCMC, and zero-inflated.

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