QQ-plots and Box-Whisker plots: where do they come from?

Published at October 15, 2020 ·  7 min read

For the most curious students QQ-plots and Box-Whisker plots usually become part of the statistical toolbox for the students attending my course of ‘Experimental methods in agriculture’. Most of them learn that the QQ-plot can be used to check for the basic assumption of gaussian residuals in linear models and that the Box-Whisker plot can be used to describe the experimental groups, when their size is big enough and we do not want to assume a gaussian distribution....

Building ANOVA-models for long-term experiments in agriculture

Published at August 20, 2020 ·  29 min read

This is the follow-up of a manuscript that we (some colleagues and I) have published in 2016 in the European Journal of Agronomy (Onofri et al., 2016). I thought that it might be a good idea to rework some concepts to make them less formal, simpler to follow and more closely related to the implementation with R. Please, be patient: this lesson may be longer than usual. What are long-term experiments?...

Fitting complex mixed models with nlme. Example #5

Published at June 5, 2020 ·  14 min read

A Joint Regression model Let’s talk about 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....

AMMI analyses for GE interactions

Published at May 12, 2020 ·  19 min read

The CoViD-19 situation in Italy is little by little improving and I feel a bit more optimistic. It’s time for a new post! I will go back to 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....

Seed germination: fitting hydro-time models with R

Published at March 23, 2020 ·  17 min read

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....

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

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. subsetting sorting casting 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....

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....