Title:

Should we transform our understanding of linearity in generalized linear models?

Generalized linear models (GLMs) are an integral part of ecological research. GLMs are able to evaluate the effect of a variable of interest for data types that are unable to be modeled using simple linear regression. They are dependent upon the ability of the data to conform to a linear predictor on a given link scale. If the data cannot, then there might be a non-linear effect of the variable in question with the response on the link scale used. However, the presence of non-linearity is not always obvious and often requires explicit testing and exploration of the data. Our primary objectives for this research were 1. to review contemporary literature on how frequently researchers take linearity into account when using GLMs; and 2. Explore the consequences of not addressing linearity for the conclusions drawn from GLMs. We reviewed ecological literature published in the last 5 years and found that ecologists do not frequently report testing their data for linearity, even when using non-linear methods. We also conducted songbird point-count surveys in Southeastern New Hampshire and used the resulting data to test the linearity assumption of occupancy models, a popular GLM. We found in that 12% of species had non-linear relationships and in one case, the inference drawn from the fit in a linear framework was opposite that concluded when fit in a non-linear framework. This research highlights the importance of linearity in GLMs and underscores the need for explicit testing for and reporting of non-linearity in ecological research.

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