An Application of Logistic Regression on Correlated Data

Abstract

It is common to find data in the form of proportions have more variability than the variance based on the binomial distribution. The phenomenon is called extra-binomial variation or overdispersion and commonly caused by the occurrence of correlation within response variable. Models for correlated outcome produces unbiased estimate, but its standard error is underestimated. Hence, confidence interval becomes too narrow and statistical test tends to reject the null hypothesis. Williams has proposed to simple method correct the effect of extra-binomial variation by taking inflation factor into consideration. In this paper, the Williams approach is implemented to analyze the poverty data in Indonesia, which exhibit extra-variation. The result shows that the method adjusts the standard error of estimates and then provides more reliable conclusion than the naive approach. Public policy of government certainly requires adequate recommendations to allocate limited resources appropriately following defined objectives. Regional data usually depends on many factors causing non-independent outcome making the data are overdispersed. Models which ignore the extra-variation will lead to a wrong conclusion. Therefore, applying regression analysis in public policy with accommodating overdispersion is important to obtain meaningful and reliable recommendations. Keywords: Logistic Regression; Extra-binomial Variation; Overdispersion; Williams Method; Poverty Analysis. 2010 Mathematics Subject Classification: 62J05