#drm

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....


Other useful functions for nonlinear regression: threshold models and all that

Published at May 1, 2021 ·  13 min read

In a recent post I presented several equations and just as many self-starting functions for nonlinear regression analyses in R. Today, I would like to build upon that post and present some further equations, relating to the so-called threshold models. But, … what are threshold models? In some instances, we need to describe relationships where the response variable changes abruptly, following a small change in the predictor. A typical threshold model looks like that in the Figure below, where we see three threshold levels:...


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....


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 useful equations for nonlinear regression in R

Published at January 8, 2019 ·  22 min read

Introduction Very rarely, biological processes follow linear trends. Just think about how a crop grows, or responds to increasing doses of fertilisers/xenobiotics. Or think about how an herbicide degrades in the soil, or about the germination pattern of a seed population. It is very easy to realise that curvilinear trends are far more common than linear trends. Furthermore, asymptotes and/or inflection points are very common in nature. We can be sure: linear equations in biology are just a way to approximate a response over a very narrow range for the independent variable....