In this paper D-optimal population designs for the simple linear random coefficients regression model with values of the explanatory variable taken from a set of equally spaced, non-repeated time points are considered. The D-optimal designs depend on the values of the variance components and locally optimal designs are therefore considered. It is shown that, if the time points are linearly transformed, then the D-optimal population designs for both the fixed effects and the variance components do not necessarily map onto one another. This result is illustrated numerically by means of a simple example.http://www.sastat.org.za/journal.htmnf201
