Ecotoxicology is not normal

Szöcs, Eduard; Schäfer, Ralf B.

doi:10.1007/s11356-015-4579-3

Cited by 38 publications

(34 citation statements)

References 38 publications

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“…Standard negative binomial tests using the χ 2 distribution had inflated type I error for small sample sizes (Fig. ), which was for the most part controlled when using resampling, as seen elsewhere (Szöcs & Schafer ). Even with residual resampling, type I error was still about 6% in small samples ( n = 16).…”

Section: Point 2 – Poor Type I Error Control Can Be Fixedmentioning

confidence: 84%

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

et al. 2016

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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.

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Section: Point 2 – Poor Type I Error Control Can Be Fixedmentioning

confidence: 84%

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

et al. 2016

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“…By comparison, the power of the fourth-corner test on the same data sets was estimated as 0.97, 0.88 and 0.88, respectively, confirming some loss of power compared to using the negative binomial LR. The negative binomial LR is costly computationally and potentially numerically unstable; for example, in our implementation using the R package mvabund (Wang et al 2012), I tried to obtain results for 1000 simulations with 999 permutation, but failed due to crashes of R. Note that the negative binomial GLM requires resampling for statistical inference as the parametric version inference is not very trustworthy, even in simple balanced design experiments for small to moderate data set sizes (Szöcs and Schäfer 2015). It would be of interest to develop a score test in the context of the negative binomial distribution.…”

Section: Discussionmentioning

confidence: 99%

“…The alternative, or rather, the complementary approach is to go the full Bayesian model-based approach with latent variables and factor analytic structure of which Warton et al (2015a) provide a nice first implementation. Even such models may need resampling methods, as even the simplest models using the negative binomial already need resampling for valid statistical inference for small to moderate data set sizes (Szöcs and Schäfer 2015). Between these extremes, there is room for GLM-and GLMM-based approaches that use row-and column-based resampling schemes for valid statistical inference.…”

Section: Discussionmentioning

confidence: 99%

Fourth-corner correlation is a score test statistic in a log-linear trait–environment model that is useful in permutation testing

Braak

2017

Environ Ecol Stat

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Ecologists wish to understand the role of traits of species in determining where each species occurs in the environment. For this, they wish to detect associations between species traits and environmental variables from three data tables, species count data from sites with associated environmental data and species trait data from data bases. These three tables leave a missing part, the fourth-corner. The fourth-corner correlations between quantitative traits and environmental variables, heuristically proposed 20 years ago, fill this corner. Generalized linear (mixed) models have been proposed more recently as a model-based alternative. This paper shows that the squared fourth-corner correlation times the total count is precisely the score test statistic for testing the linear-by-linear interaction in a Poisson log-linear model that also contains species and sites as main effects. For multiple traits and environmental variables, the score test statistic is proportional to the total inertia of a doubly constrained correspondence analysis. When the count data are over-dispersed compared to the Poisson or when there are other deviations from the model such as unobserved traits or environmental variables that interact with the observed ones, the score test statistic does not have the usual chi-square distribution. For these types of deviations, row-and column-based permutation methods (and their sequential combination) are proposed to control the type I error without undue loss of power (unless no deviation Handling Editor: Pierre Dutilleul. is present), as illustrated in a small simulation study. The issues for valid statistical testing are illustrated using the well-known Dutch Dune Meadow data set.

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“…Finally, we considered only continuous responses that were normally distributed on some scale. Non‐normally distributed responses would need to be modelled under other distributional assumptions . It should be noted that the same problems of aligning the statistical model with the experimental design exist and the same type of solutions are available , , …”

Section: Discussionmentioning

confidence: 99%

“…Non-normally distributed responses would need to be modelled under other distributional assumptions. [16][17][18] It should be noted that the same problems of aligning the statistical model with the experimental design exist and the same type of solutions are available. 14,19,20 In conclusion, for experiments in which treatments are randomly assigned to plots within blocks and observations are taken on individual units sampled from the plots, always include random block and plot effects in the analysis.…”

Section: Discussionmentioning

confidence: 99%