The effect of covariance structure on variance estimation in balanced growth-curve models with random parameters. (English) Zbl 0678.62070

Intuition suggests that altering the covariance structure of a parametric model for repeated-measures data alters the variances of the model’s estimated mean parameters. The purpose of this article is to sharpen such intuition for a family of growth-curve models with differing numbers of random effects for the individual sampling units and with a fixed structure on the mean. For every member of this family, the maximum likelihood (ML) estimator of the fixed effects is identical to the ordinary least squares (OLS) estimator. In addition, simple closed-form ML and restricted maximum likelihood estimators for the variance and covariance parameters exist for every member. As a consequence, closed- form expressions for the estimated variance-covariance matrix of the OLS estimator of the fixed effects also exist for the entire family. We derive explicit relationships between the variance and covariance parameter estimators from different members of the family and thereby extend some familiar results.


62J10 Analysis of variance and covariance (ANOVA)
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