Hello,
I recently analysed count data (in this case the no of stems per tree) using a GLM. The analysis was carried out on both log transformed and square root transformed data. Although most report that the square root transformation should be used on count data, I got a model with higher R2 and lower error values when carried out on the log transformed data. Which would you recommend I report on?
Regards
Glen
Honestly, using a square root transformation for count data is antiquated. The better approach is use a model appropriate for count data such as Poisson regression, negative binomial regression, and others.
That being said, if a transformation is used, there is nothing magical about using a square root transformation for count data. If any transformation allows a better approximation of the assumptions of the model you are using, it is better than another transformation.
A transformation should not be chosen based on the r-square. It should be based on meeting the assumptions of the model. If you are using a general linear model, the assumptions include normality of the residuals, homoscedasticity, and others.
To return to my first point: There are other reasons why count data is not appropriate for a general linear model, for example that the dependent variable isn't continuous, and is probably bound at the lower end (That is, you usually can't have counts below zero). So, it is better to use a more appropriate model, but if a transformation meets model assumptions reasonably well, one may find that to be the most reasonable approach.
Thank you very much for your helpful and detailed answer! I will investigate poisson and negative binomial regression as first choice.
You said you used a GLM. If tthis is for generalized linear model,* then of what family? There are GLMs for count data: the GLMs of the Poisson family and the negative-binomial family. These models usually employ the log-link function, what means that they estimate the log of the expectation (i.e. instead of transforming the data, the models work on the transformed expectation). The Poisson family GLM is fine when the mean is similar to the variance. In practice, the variance is often larger than the mean (->"over-dispesion"), and in such cases the negative-binomial GLM is usually a good choice (a quasi-Poisson model would be another option, but the interpretation of the former is easier, as far as I understand, because it can be derived as a Poisson model with uncertainty about the rate parameter).
*The used abbreviations are a bit ambigious. The general linear model is often simply abbreviated LM, and GLM is for the generalized linear model. The LM is essentially a GLM of the normal family with identity link.
Dear sir. I appreciate your very informative answer. I used a general linear model procedure where the treatments were assigned as the random effects and the replication as the fixed effect (using the Statgraphics package).
It is untypical that treatments are modelled by a random effect. This would mean that you consider the treatments as some selection of possible treatments that do affect the response, but that the particular treatment effect are not interesting. But I am not sure if I got this right.
The treatments are considered random effects in this case as they are a random selection of trees representing different families (the tmts) in a tree breeding trial. ie we are testing the performance of a selected tree based on the performance of a sample of its progeny.
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