THE ESTIMATION OF FIXED EFFECTS IN A MIXED LINEAR MODEL

The estimation of fixed effects is considered for small, unbalanced, mixed linear models. The two-stage estimator, in which the variance components are first estimated by ML or REML, is compared to the intra-block (IB) estimator, the ordinary least squares (OLS) estimator (ignoring the random effects) and the Gauss-Markov (GM) estimator. Comparison is made, based on 100 simulated data sets each, for 6 designs (3 BIBD\u27s and 3 unbalanced designs). In comparing loss of information, relative to the GM lower bound, the two-stage procedures (using either ML or REML) are recommended for all but the smallest and least balanced design. The study also compared estimates of the variance of the two-stage estimators, using either the GM lower bound or the Kackar-Harville (KH) approximation. Estimators of the variance using REML estimates of the variance components are recommended, since estimators using ML estimates were seriously biased downward for all designs considered

Factor analytic mixed models for the provision of grower information from national crop variety testing programs

Crop variety testing programs are conducted in many countries world-wide. Within each program, data are combined across locations and seasons, and analysed in order to provide information to assist growers in choosing the best varieties for their conditions. Despite major advances in the statistical analysis of multi-environment trial data, such methodology has not been adopted within national variety testing programs. The most commonly used approach involves a variance component model that includes variety and environment main effects, and variety by environment (V×E ) interaction effects. The variety predictions obtained from such an analysis, and subsequently reported to growers, are typically on a long-term regional basis. In Australia, the variance component model has been found to be inadequate in terms of modelling V×E interaction, and the reporting of information at a regional level often masks important local V×E interaction. In contrast, the factor analytic mixed model approach that is widely used in Australian plant breeding programs, has regularly been found to provide a parsimonious and informative model for V×E effects, and accurate predictions. In this paper we develop an approach for the analysis of crop variety evaluation data that is based on a factor analytic mixed model. The information obtained from such an analysis may well be superior, but will only enhance industry productivity if mechanisms exist for successful technology transfer. With this in mind, we offer a suggested reporting format that is user-friendly and contains far greater local information for individual growers than is currently the case