379 – Sampling Theory and Practice: Celebrating J.N.K. Rao's 75th Birthday
Extensions of Rao-Scott Tests: Fitting GLMs with Survey Data
Thomas Lumley
University of Auckland
Alastair John Scott
University of Auckland
Data from complex surveys are being used increasingly to build the same sort of explanatory and predictive models used in the rest of statistics. Unfortunately the assumptions underlying standard statistical methods are not even approximately valid for most survey data. The problem of parameter estimation has been largely solved through the use of weighted estimating equations, and software for most standard statistical procedures is now available in the major statistical packages. With one notable exception, a big gap in the output from these packages is an analogue of the likelihood ratio test and related quantities like AIC. The exception is the Rao-Scott test for log-linear models in contingency tables. It turns out to be straightforward to extend this test to many other situations, in particular to Generalized Linear Models. We show that the asymptotic null distribution of a natural analogue of the likelihood-ratio statistic is a linear combination of chi-squared random variables whose coef�cients are eigenvalues of a matrix product that does not involve the inverse of the estimated co-variance matrix.
