#Mixed_models

Fitting 'complex' mixed models with 'nlme': Example #2

Published at September 13, 2019 ·  9 min read

A repeated split-plot experiment with heteroscedastic errors Let’s imagine a field experiment, where different genotypes of khorasan wheat are to be compared under different nitrogen (N) fertilisation systems. Genotypes require bigger plots, with respect to fertilisation treatments and, therefore, the most convenient choice would be to lay-out the experiment as a split-plot, in a randomised complete block design. Genotypes would be randomly allocated to main plots, while fertilisation systems would be randomly allocated to sub-plots....


Fitting 'complex' mixed models with 'nlme': Example #3

Published at September 13, 2019 ·  11 min read

Accounting for the experimental design in regression analyses In this post, I am not going to talk about real complex models. However, I am going to talk about models that are often overlooked by agronomists and biologists, while they may be necessary in several circumstances, especially with field experiments. The point is that field experiments are very often laid down in blocks, using split-plot designs, strip-plot designs or other types of designs with grouping factors (blocks, main-plots, sub-plots)....


Fitting 'complex' mixed models with 'nlme': Example #4

Published at September 13, 2019 ·  10 min read

Testing for interactions in nonlinear regression Factorial experiments are very common in agriculture and they are usually laid down to test for the significance of interactions between experimental factors. For example, genotype assessments may be performed at two different nitrogen fertilisation levels (e.g. high and low) to understand whether the ranking of genotypes depends on nutrient availability. For those of you who are not very much into agriculture, I will only say that such an assessment is relevant, because we need to know whether we can recommend the same genotypes, e....


Fitting 'complex' mixed models with 'nlme'. Example #1

Published at August 20, 2019 ·  9 min read

The environmental variance model Fitting mixed models has become very common in biology and recent developments involve the manipulation of the variance-covariance matrix for random effects and residuals. To the best of my knowledge, within the frame of frequentist methods, the only freeware solution in R should be based on the ‘nlme’ package, as the ‘lmer’ package does not easily permit such manipulations. The ‘nlme’ package is fully described in Pinheiro and Bates (2000)....


Genotype experiments: fitting a stability variance model with R

Published at June 6, 2019 ·  8 min read

Yield stability is a fundamental aspect for the selection of crop genotypes. The definition of stability is rather complex (see, for example, Annichiarico, 2002); in simple terms, the yield is stable when it does not change much from one environment to the other. It is an important trait, that helps farmers to maintain a good income in most years. Agronomists and plant breeders are continuosly concerned with the assessment of genotype stability; this is accomplished by planning genotype experiments, where a number of genotypes is compared on randomised complete block designs, with three to five replicates....


Dealing with correlation in designed field experiments: part II

Published at May 10, 2019 ·  16 min read

With field experiments, studying the correlation between the observed traits may not be an easy task. Indeed, in these experiments, subjects are not independent, but they are grouped by treatment factors (e.g., genotypes or weed control methods) or by blocking factors (e.g., blocks, plots, main-plots). I have dealt with this problem in a previous post and I gave a solution based on traditional methods of data analyses. In a recent paper, Piepho (2018) proposed a more advanced solution based on mixed models....