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Local Estimation of Age‐Dependent Variance Components from Longitudinal Twin Data
Author(s) -
Huggins Richard
Publication year - 2000
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2000.00537.x
Subject(s) - covariance , covariance function , mathematics , smoothing , parametric statistics , statistics , kernel smoother , smoothing spline , parametric model , analysis of covariance , kernel (algebra) , econometrics , computer science , kernel method , artificial intelligence , combinatorics , radial basis function kernel , support vector machine , bilinear interpolation , spline interpolation
Summary. 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 estimating the mean function. Various parametric models for covariance structures have been proposed but, e.g., in studies of children where growth spurts occur at various ages, it is difficult to a priori determine an appropriate parametric model for the covariance structure. In particular, there is a general lack of the visualization procedures, such as lowess, that are invaluable in the initial stages of constructing a parametric model for a mean function. Here we use kernel smoothing to modify a cross‐sectional approach based on the sample covariance matrices to obtain smoothed estimates of the genetic and environmental variances and correlations for longitudinal twin data. The methods are proposed t o be exploratory as an aid to parametric modeling rather than inferential, although approximate asymptotic standard errors are derived in the Appendix.