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An additive growth curve model with orthogonal design matrices is proposed inwhich observations may have different profile forms. The proposed model allowsus to fit data and then estimate parameters in a more parsimonious way than thetraditional growth curve model. Two-stage generalized least-squares estimatorsfor the regression coefficients are derived where a quadratic estimator for thecovariance of observations is taken as the first-stage estimator. Consistency,asymptotic normality and asymptotic independence of these estimators areinvestigated. Simulation studies and a numerical example are given toillustrate the efficiency and parsimony of the proposed model for modelspecifications in the sense of minimizing Akaike's information criterion (AIC).

Estimation for an additive growth curve model with orthogonal design matrices