Published in 1999 in Biometrics 55: 102-110.
A semi-parametric mixed effects regression model is proposed for the analysis of clustered or longitudinal data with continuous, ordinal or binary outcome. The commonly used Gaussian assumption on the random effects distribution is relaxed as the partial predictive recursion method (Newton and Zhang, 1996) is used to estimate the random effects density function. The parameter estimates are obtained by maximizing the marginal profile likelihood by Powell's conjugate direction search method. The algorithm is optimized by estimating the density function of the random effects only at a few points selected according to Gauss-Legendre quadrature. Monte Carlo results are presented to evaluate this method and compare the results to estimates from the Gaussian mixed effects model. We demonstrate the usefulness of the method in the analysis of data from the Wisconsin sleep survey. The proposed method is computationally feasible for large data sets.
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