Binary Logistic Regression Modeling using Bayesian method: Analysis and Simulation on the Poverty Percentage of Districts in East Java

Achmad Efendi, Restilia Anggita Sari, Samingun Handoyo, Nur Silviyah Rahmi, Friansyah Gani

Abstract


In conducting logistic regression modeling, parameter estimation is considered an important stage. Determination of parameter estimates is often influenced by sample size and data characteristics. To cope with this issue, the Bayesian method is used as it is expected to be more robust, for instance to small sample size. In this method, MCMC is used to determine parameter values that are difficult to solve analytically. The study aims at determining the binary logistic regression model and its application to determine the factors that influence the percentage of city/district poverty rates in East Java in 2023. East Java was chosen because it has the highest percentage of poverty rates in Indonesia. This study uses informative and non-conjugate priors which is normal distribution in this case. Based on the results of the MCMC simulation with the Gibbs Sampling Algorithm, the random sample of study converged at the 266, 000th iteration with a burn-in of 60, 000 and a thin of 10. The results of this study indicate that the variables influencing the percentage of the poverty rate of cities/regencies in East Java are the Human Development Index (HDI), Life Expectancy (LE), and Gini Ratio (GR) which have significant effects. The residual deviance value shows a number that is smaller than the chi-square value. This means that the resulting model is appropriate. The model can predict data correctly by 84.2%. Simple simulations are carried out with different observed sample sizes. The simulation results show that the Bayesian method is somewhat better than likelihood estimation, particularly for data with small samples. Furthermore, we suggest the government of East Java would have more concern on HDI, LE, and GR as well as other factors related to them for poverty reduction policies.


Keywords


Bayesian; likelihood; logistic regression; poverty level; simulation

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References


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DOI: https://doi.org/10.18860/cauchy.v11i1.41326

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