Multivariate analyses of complex survey data often make extensive use of estimators of the variance-covariance matrix V of a random vector G, say, where the variances and covariances are evaluated with respect to the sample design and other sources of random variability. For example, is often used in computation of quadratic-form test statistics for Wald tests and Rao-Scott modifications of customary Pearson tests. In addition, and related design effect matrices are often used to assess the relative efficiencies of competing survey procedures. However, these analyses can be problematic when is based on a small or moderate number of degrees of freedom. This paper considers methods for approximation of V, and for computation of associated modified estimators of V. Principal emphasis is placed on exploratory analysis of the eigenvalues and eigenvectors of estimated design effect and misspecification effect matrices; and on related issues of inferential power. Some of the proposed diagnostics are applied to data from the Third National Health and Nutrition Examination Survey (NHANES III) and the Consumer Expenditure Survey (CEQ/D).

This is collaborative work with Sangrae Lee and Amang Sukasih.