An Alternative Method for Small Sample Inference with Correlated Binary Data

• Activity Number: 40
• Type: Contributed
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Health Policy Statistics*
• Author(s): Daniel McCaffrey*+ and Robert Bell
• Affiliation(s): RAND Corporation and AT&T Labs - Research
• Keywords: logistic regression ; generalized estimating equations ; bias reduced linearization ; complex samples

Abstract

Empirical sandwich estimators are used often for estimating standard errors of logistic regression models fit to data with correlated observations nested within units. Sandwich estimators tend to be too small when the number of units is small. Previously, we proposed a method for reducing the bias in sandwich estimators for linear models (Bell and McCaffrey 2001). In the current paper, we extend our method to logistic regression. Sandwich estimators rely on the sum over units of the outer-products of the vectors of quasi-score functions. The quasi-score vector for a unit equals the product of the matrix of covariates and a vector of estimated residuals. The variance-covariance matrix of the estimated residuals does not match that of the true residuals. Our estimator adjusts the estimated residuals so that their variance-covariance matrix better matches that of the true residuals. We show via simulation that our new method increases standard errors relative to the sandwich estimator yielding improved small sample inference. We compare our estimator to the alternative of Mancl and DeRouen (2001) and apply it to a group-randomized evaluation of a mental health service intervention.