Local estimation of age-dependent variance components from longitudinal twin data

In the study of longitudinal twin and family data, interest is often in the covariance structure of the data and the decomposition of this covariance structure into genetic and environmental components rather than in estimati ng the mean function. Various parametric models for covariance structures h ave been proposed but, e.g., in studies of children where growth spurts occ ur at various ages, it is difficult to a priori determine an appropriate pa rametric model for the covariance structure. In particular, there is a gene ral lack of the visualization procedures, such as lowess, that are invaluab le in the initial stages of constructing a parametric model for a mean func tion. Here we use kernel smoothing to modify a cross-sectional approach bas ed on the sample covariance matrices to obtain smoothed estimates of the ge netic and environmental variances and correlations for longitudinal twin da ta. The methods are proposed to be exploratory as an aid to parametric mode ling rather than inferential, although approximate asymptotic standard erro rs are derived in the Appendix.