Model diagnostic tests for selecting informative correlation structure in correlated data

In the generalized method of moments approach to longitudinal data analysis, unbiased estimating functions can be constructed to incorporate both the marginal mean and the correlation structure of the data. Increasing the number of parameters in the correlation structure corresponds to increasing the number of estimating functions. Thus, building a correlation model is equivalent to selecting estimating functions. This paper proposes a chi-squared test to choose informative unbiased estimating functions. We show that this methodology is useful for identifying which source of correlation it is important to incorporate when there are multiple possible sources of correlation. This method can also be applied to determine the optimal working correlation for the generalized estimating equation approach.