The Effect of Overdispersion on Logistic Regression Analysis of Poverty in Indonesia

Abstract

This paper is to show the effect of overdispersion or extra-binomial variation in logistic regression. It is common to find data in the form of proportions have more variability than the theory based on binomial distribution. Overdispersion is commonly caused by the occurrence of variation in the response probabilities or correlation within response variable. Model with overdispersion produces unbiased estimate, but its standard error is underestimated. Hence, confidence interval becomes narrow and statistical test tends to reject null hypothesis. Williams proposed to correct the effect of overdispersion by taking inflation factor into consideration. The approach is implemented to analyze poverty data in Indonesia, which exhibit overdispersion. The result showed that the method adjusted the standard error of estimates and then provided more precise conclusion than standard logistic model did. Public policy of government certainly requires adequate statistical method to allocate limited resources appropriately in order to, for example, alleviate number of poverty. Regional data usually depends on many factors causing non-independent outcome making the data are overdispersed. Therefore, applying regression analysis in public policy with accommodating overdispersion is extremely important to obtain meaningful and reliable recommendations.