Statistical Analysis

We used a generalized linear mixed model (Agresti, 2014), with a fixed effect for the percent of developed land (hereafter, developed), a fixed effect factor for year (year), and a random effect for transect (transect). Including the random effect for the transect indicates that we expect dependence within the same spatial regions on a local scale. In other words, the elk are likely to be found in areas where they have been found before, i.e. there is spatial dependence. It is arguable that the years during which the elk were surveyed could also have temporal dependence, but since the years of surveying were so dispersed (with 5 year intervals) we believe that these could be treated independently. A finer scale analysis with single year to year spatial and temporal dependence could be an interesting extension of this analysis.

The following formula shows the general form of the model:

Model Fitting:

The model was approximated in R using the lme4 software package (Bates et al, 2014). Because of the small set of predictors in the model, the information criterion approach of multi-model inference was not used (Burnham and Anderson, 2002). Rather, we fit the model which ultimately represented our understanding of the system as described above (Verhoef, 2014).

The following table shows the variables and type that were used in the analysis.