This article discusses estimates of variance for two-stage models. We present the sandwich estimate of variance as an alternative to the Murphy–Topel estimate. The sandwich estimator has a simple formula that is similar to the formula for the Murphy–Topel estimator, and the two estimators are asymptotically equal when the assumed model distributions are true. The advantages of the sandwich estimate of variance are that it may be calculated for the complete parameter vector, and that it requires estimating equations instead of fully specified log likelihoods.
BinderD. A.1983. On the variances of asymptotically normal estimators from complex surveys. International Statistical Review51: 279–292.
2.
CarrollR. J., and KauermannG.2002. The sandwich variance estimator: Efficiency properties and coverage probability of confidence intervals. Journal of the American Statistical Association submitted.
3.
GreeneW.2000. Econometric Analysis.4th ed. Upper Saddle River, NJ: Prentice-Hall.
4.
HuberP. J.1967. The behavior of maximum likelihood estimates under nonstandard conditions. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, 221–233. Berkeley, CA: University of California Press.
5.
LiangK.-Y., and ZegerS.L.1986. Longitudinal data analysis using generalized linear models. Biometrika73: 13–22.
6.
MurphyK. M., and TopelR.H.1985. Estimation and inference in two-step econometric models. Journal of Business and Economic Statistics3(4): 370–379.
7.
StefanskiL. A., and BoosD.D.2002. The calculus of M-estimation. The American Statistician56(1): 29–38.
