Table 1. Empirical illustration of uninformative parameters.
Here, I illustrate uninformative parameters from a real example derived from analyses in Yalcin and Leroux [26]. The objective of this study was to assess the relative and combined effects of land-use change and climate change on the colonization and extinction of species. We used a case study in Ontario, Canada where birds were surveyed in standardized grids during two time periods (1981–1985 and 2001–2005). Below I provide results for a subset of the colonization models of one of the study species, black-throated blue warbler (Setophaga caerulescens). In the colonization model, the black-throated blue warbler is observed as absent in a grid in the first time period and the response is warbler absence (0) or presence (1) in the second time period. Yalcin and Leroux [26] selected covariates based on a priori hypotheses. These covariates measured changes in land-use (% change in land-cover in each grid (%LCC), % change in land-cover in 20km buffers surrounding each grid (%LCCb) and change in Net Primary Productivity (ΔNPP)) and climate (change in mean winter temperature (ΔMWT), change in mean summer temperature (ΔMST), and change in mean winter precipitation (ΔMWP)) during the time period between bird sampling. All models include sampling effort (SE) in order to control for variable sampling effort across grids and between time periods. Yalcin and Leroux [26] fit generalized linear models with a binomial error structure and a logit link for local colonization models for the black-throated blue warbler. See [26] for full details on data, methods, and hypotheses pertaining to each covariate used in these models. Table 1 provides a summary of AIC model selection results and parameter estimates (95% Confidence Interval) for a sub-set of the colonization models considered for this species. The first set of columns are the model covariates (abbreviations defined above) and the second set of columns are model selection information (K = number of estimated parameters, log L = model log-likelihood, ΔAICC = Difference in AICC between the top ranked model (i.e., model with lowest AICC) and current model, Pseudo R2 = McFadden’s pseudo R2). Each row is a different model and blank values for a covariate means that this particular model did not include this covariate. By following the decision tree in Fig 1, Yalcin and Leroux [26] identified the variable %LCCb is an uninformative parameter in models 2, 4, and 6 (bold).
| Model covariates | Model selection | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Model | SE | ΔNPP | %LCC | %LCCb | ΔMST | ΔMWT | ΔMWP | K | log L | ΔAICC | Pseudo R2 |
| 1 | 0.30 (0.24,0.39) |
0.06 (0.03,0.09) |
0.04 (0.02,0.06) |
0.25 (0.10,0.40) |
-2.54 (-4.64,-0.46) |
6 | -276.14 | 0.00 | 0.28 | ||
| 2 | 0.30 (0.24,0.39) |
0.06 (0.03,0.09) |
0.04 (0.01,0.06) |
0.00 (-0.05,0.05) |
0.25 (0.10,0.41) |
-2.54 (-4.65,-0.47) |
7 | -276.14 | 2.00 | 0.28 | |
| 3 | 0.30 (0.22,0.39) |
0.05 (0.02,0.08) |
0.25 (0.10,0.41) |
-2.06 (-4.23,-0.09) |
0.07 (0.02,0.12) |
6 | -278.18 | 4.07 | 0.27 | ||
| 4 | 0.30 (0.22,0.38) |
0.05 (0.02,0.08) |
0.03 (-0.02,0.07) |
0.29 (0.12,0.45) |
-2.04 (-4.23,-0.12) |
0.07 (0.01,0.12) |
7 | -277.63 | 4.97 | 0.27 | |
| 5 | 0.30 (0.22,0.38) |
0.06 (0.04,0.09) |
0.32 (0.18,0.46) |
0.08 (0.03,0.13) |
5 | -279.95 | 5.61 | 0.26 | |||
| 6 | 0.30 (0.22,0.38) |
0.06 (0.04,0.09) |
0.03 (-0.02,0.07) |
0.35 (0.20,0.50) |
0.08 (0.03,0.13) |
6 | -279.34 | 6.39 | 0.26 | ||
| Intercept | 1 | -344.09 | 125.91 | 0.00 | |||||||