A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.Comment: Accepted for publication in Statistics and Computin

Growth increments and stability over time in fast-growing forest tree species

Zamudio, F. Facultad de Ciencias Forestales, Universidad de Talca, PO Box 747, 2 Norte 685, Talca, Chile.We review an analytical procedure useful for measuring the influence of time on the phenotypic expression of cumulative growth. It consists of separating the genetic control into two meaningful components: the cumulative genetic effect of growth increments and the effect of genotype × time interaction. The analysis is performed via a hierarchical mixed linear model. Data from three Pinus tecunumanii Eguiluz & J.P. Perry provenance–progeny trials established by the CAMCORE Cooperative in South America were used to assess the practical application of the method. Results suggest that the simple observation of age–age correlations for cumulative growth can be misleading, because they hide the effects of family and within-family variation. The partition of cumulative growth into mutually exclusive growth increments can help to discriminate covariance components, which are also useful to predict the degree of association between growth at different ages and the potential value for early selection