Use of robust variance components models to analyse triglyceride data in families

A robust approach for analysis of variance components models is presented which does not rely on the assumption of multivariate normality for its validity. This approach uses the multivariated normal distribution as a 'working model' but obtains standard errors for the final estimators which do not depend on this underlying distribution. By using the observed variance in the first derivatives of the multivariate normal 'working model' to modify the conventional score test, hypotheses regarding specific components can also be tested without relying directly on the assumption of multivariate normality. A special case is presented where both the modified score test and the likelihood ratio test are equally robust, and simulated data are used to illustrate this situation. Measurements of triglyceride levels in 391 individuals in 60 families randomly selected from the membership of a health maintenance organization are used to illustrate this robust approach to variance components.