Three points to consider when choosing a LM or GLM test for count data

Abstract

Summary1. The two most common approaches for analysing count data are to use a generalized linear model (GLM), or transform data, and use a linear model (LM). The latter has recently been advocated to more reliably maintain control of type I error rates in tests for no association, while seemingly losing little in power. We make three points on this issue. 2. Point 1 -Choice of statistical model should primarily be made on the grounds of data properties. Choice of testing procedure should be considered and addressed as a separate issue, after model choice. If models with the appropriate data properties nonetheless have statistical problems such as type I error control (i.e. type I error rate greatly exceeds the intended significance level), the best solution is to keep the model but fix the problems. 3. Point 2 -When a test has problems with type I error control, it can usually be corrected, but this may require departure from software default approaches. In particular, resampling is a good solution for small samples that can be easy to implement. 4. Point 3 -Tests based on models that better fit the data (e.g. a negative binomial for overdispersed count data) tend to have better power properties and in some instances have considerably higher power. 5. We illustrate these issues for a 2 9 2 experiment with a count response. This seemingly simple problem becomes hard when the experimental design is unbalanced, and software default procedures using LMs or GLMs can have difficulties, although in both cases the issues can be fixed. 6. We conclude that, when GLMs are thought to fit count data well, and when any necessary steps are taken to correct type I error rates, they should be used rather than LMs. Nonetheless, standard LM tests are often robust and can have good type I error control, so there is an argument for their use for counts when diagnostics are difficult and statistical models are complex, although at some risk of loss of power and interpretability.

Moving beyond presence and absence when examining changes in species distributions

“…We addressed these questions by simulating the abundance of a species population (M) using a negative binomial model (O'Hara & Kotze, 2010;Lind en & M€ antyniemi, 2011;Warton et al, 2016) and then once again randomly sampling n individuals from an overall community of size N using a hypergeometric distribution. By repeating this 10 000 times, we were able to examine how the probability of occurrence in the sample, P(m > 0), related to the expected relative abundance of the species in the overall community (M/N).…”

Count data in biology—Data transformation or model reformation?

“…Yet, Warton et al. () underlined the importance of choosing an appropriate model based on data properties and diagnostic tools, which can be more difficult with small sample sizes. Warton et al.…”

“…Warton et al. () as well as Ives () and Stroup () used simulated data in their analyses, for which the error structure and true values of the parameter estimates are known; they did not extend their analyses to case studies where the error structure is unknown.…”

Edge effects on beetle assemblages in an Atlantic forest fragment and pasture in Sergipe, Brazil

“…These models are suitable for ecological data of richness and abundance due the count data nature (Warton et al 2016). All the models were submitted to the residual analysis to verify the suitable error distribution.…”