Here is why I don't care about the Levene's test

Published at March 15, 2024 ·  5 min read

During my stat courses, I never give my students any information about the Levene’s test (Levene and Howard, 1960), or other similar tests for homoscedasticity, unless I am specifically prompted to do so. It is not that I intend to underrate the tremendous importance of checking for the basic assumptions of linear model! On the contrary, I always show my students several methods for the graphical inspection of model residuals, but I do not share the same aching desire for a P-value, that most of my colleagues seem to possess....

Pairwise comparisons in nonlinear regression

Published at February 23, 2024 ·  8 min read

Pairwise comparisons are one of the most debated topic in agricultural research: they are very often used and, sometimes, abused, in literature. I have nothing against the appropriate use of this very useful technique and, for those who are interested, some colleagues and I have given a bunch of (hopefully) useful suggestions in a paper, a few years ago (follow this link here). According to the emails I often receive, there might be some interest in making pairwise comparisons in linear/nonlinear regression models....

GGE analyses for multi-environment studies

Published at May 31, 2023 ·  12 min read

In a recent post we have seen that we can use Principal Component Analyses (PCA) to elucidate the ‘genotype by environment’ relationship (see this post). Whenever the starting point for PCA is the doubly-centered (centered by rows and columns) matrix of yields across environments, we talk about AMMI analysis, which is often used to get insight into the stability of genotype yields across environments. By changing the starting matrix, we can obtain a different perspective and put focus on the definition of macroenvironments and on the selection of winning genotypes....

AMMI analyses for multi-environment studies

Published at May 26, 2023 ·  19 min read

Again into a subject that is rather important for most agronomists, i.e. the selection of crop varieties. All farmers are perfectly aware that crop performances are affected both by the genotype and by the environment. These two effects are not purely additive and they often show a significant interaction. By this word, we mean that a genotype can give particularly good/bad performances in some specific environmental situations, which we may not expect, considering its average behaviour in other environmental conditions....

Why are derivatives important in life? A case-study with nonlinear regression

Published at June 9, 2021 ·  7 min read

In general, undergraduate students in biology/ecology courses tend to consider the derivatives as a very abstract entity, with no real usefulness in the everyday life. In my work as a teacher, I have often tried to fight against such an attitude, by providing convincing examples on how we can use the derivatives to get a better understanding about the changes on a given system. In this post I’ll tell you about a recent situation where I was involved with derivatives....

The R-squared and nonlinear regression: a difficult marriage?

Published at March 25, 2021 ·  4 min read

Making sure that a fitted model gives a good description of the observed data is a fundamental step of every nonlinear regression analysis. To this aim we can (and should) use several techniques, either graphical or based on formal hypothesis testing methods. However, in the end, I must admit that I often feel the need of displaying a simple index, based on a single and largely understood value, that reassures the readers about the goodness of fit of my models....

Pairwise comparisons in nonlinear regression

Published at January 19, 2021 ·  6 min read

Pairwise comparisons are one of the most debated topic in agricultural research: they are very often used and, sometimes, abused, in literature. I have nothing against the appropriate use of this very useful technique and, for those who are interested, some colleagues and I have given a bunch of (hopefully) useful suggestions in a paper, a few years ago (follow this link here). Pairwise comparisons usually follow the application of some sort of linear or generalised linear model; in this setting, the ‘emmeans’ package (Lenth, 2020) is very handy, as it uses a very logical approach....

A collection of self-starters for nonlinear regression in R

Published at February 26, 2020 ·  29 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....

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....

Companion R Packages

Published at May 30, 2019 ·  1 min read

This blog is supported by a few R packages containing all functions, datasets and other utilities, which are necessary to work through posts, tutorials and books. The packages are: statforbiology aomisc AgriCensData drcSeedGerm drcte lmDiallel The three packages ‘drcSeedGerm’, ‘drcte’ and ‘lmDiallel’ are already hosted on CRAN and they can be installed from within RStudio, by using the usual ‘install.package()’ function. For all packages, the development versions are hosted on gitHub and they can be installed from there....