Testing Inference from Logistic Regression Models in Data with Unobserved Heterogeneity at Cluster Levels

Abstract

Clustering due to unobserved heterogeneity may seriously impact on inference from binary regression models. We examined the performance of the logistic, and the logistic-normal models for data with such clustering. The total variance of unobserved heterogeneity rather than the level of clustering determines the size of bias of the maximum likelihood (ML) estimator, for the logistic model. Incorrect specification of clustering as level 2, using the logistic-normal model, provides biased estimates of the structural and random parameters, while specifying level 1, provides unbiased estimates for the former, and adequately estimates the latter. The proposed procedure appeals to many research areas.

Keywords:

• Biased estimates
• Casual inference
• Cluster
• Logistic model
• Logistic-Normal model
• Unobserved heterogeneity

Mathematics Subject Classification:

• 62J12
• 62P10

Acknowledgments

I am grateful to professor D. Holt for the advice and suggestions he gave to the original study. I am very grateful to Dr. Marie South and Dr. Peter Egger for a considerable help with the FORTRAN programmes used in the simulation.

Notes

Note: Reject %: the number of times in percentage that the true parameter lied outside the 95% confidence intervals of the simulated estimator. Estimates are based on 200 simulations. J = 12 (replication at level 2), and K = 2 (replication at level 1), n = 768 individuals, for (α, β) = (− 1, 2).