A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution then requires an integral equation that is of dimension equal to the number of nonlinear terms. For nonlinear functions that have linear coefficients, the improvement in computational speed and accuracy using the new algorithm can be dramatic. An illustration of the method with repeated measures data from a learning experiment is presented.

Alfalfa seed yield and Canada thistle densities were measured in 10 fields in southern Alberta to assess the effect of thistles on seed yield. Thistle density and seed yield from each field were fitted to the Weibull, hyperbolic, and linear equations and a random coefficient and linear equation were used to obtain an “average yield loss curve”. Estimated average losses in alfalfa seed yield were >34% and >48% at thistle densities of 10 and 20 shoots m–2, respectively.