Plotting weather data with ggplot()

Published at June 6, 2024 ·  7 min read

Very often, we agronomists have to deal with weather data, e.g., to evaluate and explain the behaviour of genotypes in different environments. We are very much used to representing temperature and rainfall data in one single graph with two y-axis, which gives a good immediate insight on the weather pattern at a certain location. Unfortunately, I had to discover that doing such graphs with ggplot() is not a straightforward task.

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. In particular, whenever we have grouped data and we have fitted the same model to each group, we might like to compare the groups, to state whether the regression lines/curves are significantly different from each other. To this aim, we could consider two approaches:

Regression analyses with common checks in pesticide research

Published at December 15, 2023 ·  4 min read

In pesticide research or, in general, agriculture research, we very commonly encounter experiments with, e.g., several herbicides tested at different doses and in different conditions. For these experiments, the untreated control is always added and, of course, such control is common to all herbicides.

For example, in another post (see here) we have considered an experiment with two herbicides (rimsulfuron and dicamba) at two rates (40 and 60 g/ha for rimsulfuron and 0.6 and 1 kg/ha for dicamba) and with four adjuvant treatments (surfactant, frigate, mineral oil and no adjuvant). The dataset is loaded in the box below: there are three predictors (Herbicide, Adjuvant and Dose) and two quantitative response variables (WeedCoverage and Yield).

Factorial designs with check in pesticide research

Published at December 15, 2023 ·  6 min read

In pesticide research or, in general, agriculture research, we very commonly encouter experiments with two/three crossed factors and some other treatment that is not included in the factorial structure. For example, let’s consider an experiment with two herbicides (rimsulfuron and dicamba) at two rates (40 and 60 g/ha for rimsulfuron and 0.6 and 1 kg/ha for dicamba) and with four adjuvant treatments (surfactant, frigate, mineral oil and no adjuvant). Apart from this fully crossed structure, we need to introduce, at least, an untreated control and a hand-weeded control. The design for such an experiment has been termed ‘augmented factorial’, because we are, indeed, including some extra treatment levels beyond the crossed factorial structure.

Repeated measures and subsampling with perennial crops

Published at December 4, 2023 ·  5 min read

In a recent post, I have talked about repeated measures, for a case where measurements were taken repeatedly in the same plots across years see here. Previously, in another post, I had talked about subsampling, for a case where several random samples were taken from the same plot see here.

Repeated measures and subsampling are vastly different: in the first case I am specifically interested in the ‘evolution’ of the response over time (or space, sometimes). In the second case (subsampling), I only want to improve the precision/accuracy of my measurements, by taking multiple random samples in each plot.

Back-transformations with emmeans()

Published at November 30, 2023 ·  5 min read

I am one of those old guys who still uses the stabilising transformations, when the data do not conform to the basic assumptions for ANOVA. Indeed, apart from counts and proportions, where GLMs can be very useful, I have not yet found a simple way to deal with heteroscedasticity for continuous variables, such as yield, weight, height and so on. Yes, I know, Generalised Least Squares (GLS) can be useful to fit heteroscedastic models, but I would argue that stabilising transformations are, conceptually, very much simpler and they can be easily thought to PhD students and practitioners, with only a basic level of knowledge about statistics.

Designed experiments with replicates: Principal components or Canonical Variates?

Published at November 2, 2023 ·  16 min read

A few days ago, a colleague of mine wanted to hear my opinion about what multivariate method would be the best for a randomised field experiment with replicates. We had a nice discussion and I thought that such a case-study might be generally interesting for the agricultural sciences; thus, I decided to take my Apple Mac-Book PRO, sit down, relax and write a new post on this matter.

My colleague’s research study was similar to this one: a randomised block field experiment (three replicates) with 16 durum wheat genotypes, which was repeated in four years. The quality of grain yield was assessed by recording the following four traits:

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. In particular, if the two-way matrix of yields across environments is only column-centered before PCA, we talk about GGE analysis (Yan et al., 2000). In spite of some academic debate (see Gauch, 2006, Yan et al., 2007, Gauch et al., 2008), AMMI and GGE analyses are both useful and can be used as two complementary tools for the analysis of multi-environment genotype data.

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. The Genotype by Environment (GE) interaction may cause changes in the ranking of genotypes, depending on the environment and may play a key role in varietal recommendation, for a given mega-environment.