Analysis of categorical data obtained by stratified random sampling

Analysis of categorical data by linear models is extended to data obtained by stratified random sampling. It is shown that, asymptotically, proportional allocation reduces the variances of estimators from those obtained hy simple random sampling. The difference between the asymptotic covariance matrices of estimated parameters obtained by simple random sampling and stratified random sampling with proportional allocation is shown to be positive definite vinder fairly non-restrictive conditions, when an asymptotically efficient method of estimation is used. Data from a major community study of mental health are used to illustrate application of the technique.