Commutative Jordan algebras play a central part in orthogonal models. We apply the concepts of genealogical tree of an Jordan algebra associated to a linear mixed model in an experiment conducted to study optimal choosing of dentist materials. Apart from the conclusions of the experiment itself, we show how to proceed in order to take advantage of the great possibilities that Jordan algebras an...

The analysis of a series of crop variety trials often proceeds using a mixed model in which the data are the combined means from individual trials. The residual variation for this model consists of genotype by environment (G.E) interactions and within trial error variation. The latter is regarded as known from the analyses of individual trials, and any associated heterogeneity can be accounted ...

With increasing competition in the business world and the emergence and development of new technologies, many companies have turned to integrated production and distribution for timely production and delivery at the lowest cost of production and distribution and with the least delay in delivery. By increasing human population and the increase in greenhouse gas emissions and industrial waste, in...

We describe the form of the linear mixed-effects and generalized linear mixed-effects models fit by lmer and give details of the representation and the computational techniques used to fit such models. These techniques are illustrated on several examples.

Example Description 1 Tracer lot stability data { classical linear mixed eeects model 2 Pill dissolution data { classical linear mixed eeects model 3 Rat pup weight data { classical linear mixed eeects model 4 CD4 trajectories { linear mixed model with nonconstant intra-subject variance 5 Soybean growth study { nonlinear mixed model with nonconstant within-plot variance 6 Population PK study of...

Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5–10 years the literature on model selection in l...