# #linear_models

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....

The coefficient of determination: is it the R-squared or r-squared?

Published at November 26, 2022 ·  9 min read

We often use the coefficient of determination as a swift ‘measure’ of goodness of fit for our regression models. Unfortunately, there is no unique symbol for such a coefficient and both $$R^2$$ and $$r^2$$ are used in literature, almost interchangeably. Such an interchangeability is also endorsed by the Wikipedia (see at: https://en.wikipedia.org/wiki/Coefficient_of_determination ), where both symbols are reported as the abbreviations for this statistical index. As an editor of several International Journals, I should not agree with such an approach; indeed, the two symbols $$R^2$$ and $$r^2$$ mean two different things, and they are not necessarily interchangeable, because, depending on the setting, either of the two may be wrong or ambiguous....

Stabilising transformations: how do I present my results?

Published at June 15, 2019 ·  5 min read

ANOVA is routinely used in applied biology for data analyses, although, in some instances, the basic assumptions of normality and homoscedasticity of residuals do not hold. In those instances, most biologists would be inclined to adopt some sort of stabilising transformations (logarithm, square root, arcsin square root…), prior to ANOVA. Yes, there might be more advanced and elegant solutions, but stabilising transformations are suggested in most traditional biometry books, they are very straightforward to apply and they do not require any specific statistical software....

How do we combine errors? The linear case

Published at April 15, 2019 ·  7 min read

In our research work, we usually fit models to experimental data. Our aim is to estimate some biologically relevant parameters, together with their standard errors. Very often, these parameters are interesting in themselves, as they represent means, differences, rates or other important descriptors. In other cases, we use those estimates to derive further indices, by way of some appropriate calculations. For example, think that we have two parameter estimates, say Q and W, with standard errors respectively equal to $$\sigma_Q$$ and $$\sigma_W$$: it might be relevant to calculate the amount:...

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