\(V\)- and \(D\)-optimal population designs for the simple linear regression model with a random intercept term. (English) Zbl 1130.62071
Summary: \(V\)- and \(D\)-optimal population designs for a simple linear regression model with a random intercept term are considered. This is done with special reference to longitudinal data, that is data measured repeatedly at specified time points. Individual designs, comprising up to \(k+1\) distinct and equally spaced values of the explanatory variable, are assumed to be available. The problem of constructing a population design which allocates weights to these individual designs in such a way that the variances associated with the mean marginal responses at a given vector of time points are in some sense minimized is addressed. \(V\)-optimal designs are obtained and a geometric approach to confirm the global optimality or otherwise of these designs is introduced. The study is extended to the \(D\)-optimal case. It is noted that the \(V\)- and \(D\)-optimal population designs are robust to the value of the intraclass correlation coefficient.
Keywords:
linear regression; longitudinal data; information matrix; equivalence theorem; population designs; \(V\)-optimality; \(D\)-optimalityReferences:
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