Accounting for the experimental design in linear/nonlinear regression analyses

Published at December 4, 2020 ·  11 min read

In this post, I am going to talk about an issue that is often overlooked by agronomists and biologists. 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). We know that these grouping factors should be appropriately accounted for in data analyses: ‘analyze them as you have randomized them’ is a common saying attributed to Ronald Fisher. Indeed, observations in the same group are correlated, as they are more alike than observations in different groups. What happens if we neglect the grouping factors? We break the independence assumption and our inferences are invalid (Onofri et al., 2010).

lmDiallel: a new R package to fit diallel models. The Hayman's model (type 1)

Published at November 26, 2020 ·  15 min read

In a previous post we have presented our new ‘lmDiallel’ package (see this link here and see also the original paper in Theoretical and Applied Genetics). This package provides an extensions to fit a class of linear models of interest for plant breeders or geneticists, the so-called diallel models. In this post and other future posts we would like to present some examples of how to use this package: please, sit back and relax and, if you have comments, let us know, using the email link at the bottom of this post.

lmDiallel: a new R package to fit diallel models. Introduction

Published at November 11, 2020 ·  7 min read

Together with some colleagues from the plant breeding group, we have just published a new paper, where we presented a bunch of R functions to analyse the data from diallel experiments. The paper is titled ‘Linear models for diallel crosses: a review with R functions’ and it is published in the ‘Theoretical and Applied Genetics’ Journal. If you are interested, you can take a look here at this link.

Diallel experiments are based on a set of possible crosses between some homozygous (inbred) lines. For example, if we have the male lines A, B and C and the female lines A, B and C (same lines used, alternatively, as male and female), we would have the following selfed parents: AA, BB and CC and the following crosses: AB, AC, BC. In some instances, we might also have the reciprocals BA, CA and CB. Selfed parents and crosses are compared on a Randomised Complete Block Design, usually replicated across seasons and/or locations.

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

Published at October 15, 2020 ·  7 min read

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.

First question: what are long-term experiments? Agricultural experiments have to deal with long-term effects of cropping practices. Think about fertilisation: certain types of organic fertilisers may give effects on soil fertility, which are only observed after a relatively high number of years (say: 10-15). In order to observe those long-term effects, we need to plan Long Term Experiments (LTEs), wherein each plot is regarded as a small cropping system, with the selected combination of rotation, fertilisation, weed control and other cropping practices. Due to the fact that yield and other relevant variables are repeatedly recorded over time, LTEs represent a particular class of multi-environment experiments with repeated measures.

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.