Analysis methods for nonlinear models with compoun- symmetric covariance

Abstract

Existing general methods for fitting nonlinear multivariate regression functions produce standard errors for parameter estimates which can be extremely optimistic when small samples are used. By incorporating the compound - symmetric covariance structure into the model where appropriate, substantial improvements in the estimation of the covariance matrix for the parameter estimates may be expected. An approximate weighted least squares method is described for fitting a nonlinear response function to repeated measures data with compound symmetric covariance for each independent sampling unit. The method is applicable to incomplete data. Under regularity conditions, the estimation procedure yields asymptotically normal, unbiased and consistent estimators. With complete Gaussian data, the procedure may be iterated to produce maximum likelihood estimates of response function parameters and variance components. Hypothesis testing following estimation procedures which either ignore or address the compound symmetry in simulated data are compared. Substantially smaller sample sizes are shown to yield the correct Type I error in the latter case

Keywords:

• incomplete data
• repeated measurements
• weighted least squares
• maximum likelihood
• Type I error