D- and V-optimal population designs for the quadratic regression model with a random intercept term |
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Authors: | Legesse Kassa Debusho Linda M Haines |
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Institution: | a Department of Statistics, University of Pretoria, Information Technology Building, Pretoria 0002, South Africa b Department of Statistical Sciences, University of Cape Town, Rondebosch 7701, South Africa |
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Abstract: | In this paper D- and V-optimal population designs for the quadratic regression model with a random intercept term and with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. D-optimal population designs based on single-point individual designs were readily found but the derivation of explicit expressions for designs based on two-point individual designs was not straightforward and was complicated by the fact that the designs now depend on ratio of the variance components. Further algebraic results pertaining to d-point D-optimal population designs where d≥3 and to V-optimal population designs proved elusive. The requisite designs can be calculated by careful programming and this is illustrated by means of a simple example. |
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Keywords: | Quadratic regression Random intercept Population designs D- and V-optimality |
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