Fitting complex mixed models with nlme. Example #5

Published at June 5, 2020 ·  14 min read

Joint Regression is a very old, but, nonetheless, useful technique. It is widely known that the yield of a genotype in different environments depends on environmental covariates, such as the amount of rainfall in some critical periods of time. Apart from rain, also temperature, wind, solar radiation, air humidity and soil characteristics may concur to characterise a certain environment as good or bad and, ultimately, to determine yield potential.

Early in the 60s, several authors proposed that the yield of genotypes is expressed as a function of an environmental index $e_j$, measuring the yield potential of each environment $j$ (Finlay and Wilkinson, 1963; Eberhart and Russel, 1966; Perkins and Jinks, 1968). For example, for a genotype $i$, we could write:

Seed germination: fitting hydro-time models with R

Published at March 23, 2020 ·  16 min read

THE CODE IN THIS POST WAS UPDATED ON JANUARY 2022

I am locked at home, due to the COVID-19 emergency in Italy. Luckily I am healthy, but there is not much to do, inside. I thought it might be nice to spend some time to talk about seed germination models and the connections with survival analysis.

We all know that seeds need water to germinate. Indeed, the absorption of water activates the hydrolytic enzymes, which break down food resources stored in seeds and provide energy for germination. As the consequence, there is a very close relationship between water content in the substrate and germination velocity: the higher the water content the quickest the germination, as long as the availability of oxygen does not become a problem (well, water and oxygen in soil may compete for space and a high water content may result in oxygen shortage).

A collection of self-starters for nonlinear regression in R

Published at February 26, 2020 ·  30 min read

Usually, the first step of every nonlinear regression analysis is to select the function $f$, which best describes the phenomenon under study. The next step is to fit this function to the observed data, possibly by using some sort of nonlinear least squares algorithms. These algorithms are iterative, in the sense that they start from some initial values of model parameters and repeat a sequence of operations, which continuously improve the initial guesses, until the least squares solution is approximately reached.

Self-starting routines for nonlinear regression models

Published at February 14, 2020 ·  8 min read

(Post updated on 17/07/2023) In R, the drc package represents one of the main solutions for nonlinear regression and dose-response analyses (Ritz et al., 2015). It comes with a lot of nonlinear models, which are useful to describe several biological processes, from plant growth to bioassays, from herbicide degradation to seed germination. These models are provided with self-starting functions, which free the user from the hassle of providing initial guesses for model parameters. Indeed, getting these guesses may be a tricky task, both for students and for practitioners.

Some everyday data tasks: a few hints with R (revisited)

Published at January 28, 2020 ·  12 min read

One year ago, I published a post titled ‘Some everyday data tasks: a few hints with R’. In that post, I considered four data tasks, that we all need to accomplish daily, i.e.

1. subsetting
2. sorting
3. casting
4. melting

In that post, I used the methods I was more familiar with. And, as a long-time R user, I have mainly incorporated in my workflow all the functions from the base R implementation.

Nonlinear combinations of model parameters in regression

Published at January 9, 2020 ·  11 min read

Nonlinear regression plays an important role in my research and teaching activities. While I often use the ‘drm()’ function in the ‘drc’ package for my research work, I tend to prefer the ‘nls()’ function for teaching purposes, mainly because, in my opinion, the transition from linear models to nonlinear models is smoother, for beginners. One problem with ‘nls()’ is that, in contrast to ‘drm()’, it is not specifically tailored to the needs of biologists or students in biology. Therefore, now and then, I have to build some helper functions, to perform some specific tasks; I usually share these functions within the ‘aomisc’ package, that is available on github (see this link).

Testing for interactions in nonlinear regression

Published at September 13, 2019 ·  11 min read

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.g., both in conventional agriculture (high nitrogen availability) and in organic agriculture (relatively lower nitrogen availability).

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

Published at September 13, 2019 ·  10 min read

In this post I am going to deal with a repeated split-plot experiment with heteroscedastic errors. Ready for this trip?

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. As usual in agricultural research, the experiment should be repeated in different years, in order to explore the environmental variability of results.

The 'Environmental Variance' model for Multi-Environment Experiments

Published at August 20, 2019 ·  9 min read

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). Of course, the ‘asreml’ package can be used, but, unfortunately, this is not freeware.

Germination data and time-to-event methods: comparing germination curves

Published at July 20, 2019 ·  11 min read

Very often, seed scientists need to compare the germination behaviour of different seed populations, e.g., different plant species, or one single plant species submitted to different temperatures, light conditions, priming treatments and so on. How should such a comparison be performed?

Let’s take a practical approach and start from an appropriate example: a few years ago, some collegues studied the germination behaviour for seeds of a plant species (Verbascum arcturus, BTW…), in different conditions. In detail, they considered the factorial combination of two storage periods (LONG and SHORT storage) and two temperature regimes (FIX: constant daily temperature of 20°C; ALT: alternating daily temperature regime, with 25°C during daytime and 15°C during night time, with a 12:12h photoperiod). If you are a seed scientist and are interested in this experiment, you’ll find detail in Catara et al. (2016).