Abstract
Ecologists and conservation biologists frequently use multipleregression (MR) to try to identify factors influencing response variables suchas species richness or occurrence. Many frequently used regression methods maygenerate spurious results due to multicollinearity. argued that there are actually two kinds of MR modelling: (1)seeking the best predictive model; and (2) isolating amounts of varianceattributable to each predictor variable. The former has attracted most attentionwith a plethora of criteria (measures of model fit penalized for modelcomplexity – number of parameters) and Bayes-factor-based methods havingbeen proposed, while the latter has been little considered, althoughhierarchical methods seem promising (e.g. hierarchical partitioning). If the twoapproaches agree on which predictor variables to retain, then it is more likelythat meaningful predictor variables (of those considered) have been found. Therehas been a problem in that, while hierarchical partitioning allowed the rankingof predictor variables by amounts of independent explanatory power, there was no(statistical) way to decide which variables to retain. A solution usingrandomization of the data matrix coupled with hierarchical partitioning ispresented, as is an ecological example.
Similar content being viewed by others
References
Anderson M.J. 2001. A new method for non-parametric multivariate analysis of variance. Australian Ecology 26: 32–46.
Bolger D.T., Alberts A.C. and Soulé M.E. 1991. Occurrence patterns of bird species in habitat fragments: sampling, extinction, and nested species subsets. American Naturalist 137: 155–166.
Buckland S.T., Burnham K.P. and Augustin N.H. 1997. Model selection: an integral part of inference. Biometrics 53: 603–618.
Burnham K.P. and Anderson D.R. 1998. Model Selection and Inference: A Practical Information-Theoretic Approach. Springer-Verlag, New York.
Chevan A. and Sutherland M. 1991. Hierarchical partitioning. The American Statistician 45: 90–96.
Christensen R. 1992. Comment on Chevan and Sutherland. The American Statistician 46: 74.
Clarke K.R. 1993. Non-parametric multivariate analyses of changes in community structure. Australian Journal of Ecology 18: 117–143.
Loyn R.H. 1987. Effects of patch area and habitat on bird abundances, species numbers and tree health in fragmented Victorian forests. In: Saunders D.A., Arnold G.W., Burbidge A.A. and Hopkins A.J.M. (eds), Nature Conservation: the Role of Remnants of Native Vegetation. Surrey Beatty and Sons, Chipping Norton, Australia, pp. 65–77.
Mac Nally R. 1996. Hierarchical partitioning as an interpretative tool in multivariate inference. Australian Journal of Ecology 21: 224–228.
Mac Nally R. 2000. Regression and model-building in conservation biology, biogeography and ecology: the distinction between — and reconciliation of — ‘predictive’ and ‘explanatory’ models. Biodiversity and Conservation 9: 655–671.
Mac Nally R., Bennett A.F. and Horrocks G. 2000. Forecasting the impacts of habitat fragmentation. Evaluation of species-specific predictions of the impact of habitat fragmentation on birds in the box-ironbark forests of central Victoria, Australia. Biological Conservation 95: 7–29.
Manly B.F.J. 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman & Hall, London.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mac Nally, R. Multiple regression and inference in ecology and conservation biology: further comments on identifying important predictor variables. Biodiversity and Conservation 11, 1397–1401 (2002). https://doi.org/10.1023/A:1016250716679
Issue Date:
DOI: https://doi.org/10.1023/A:1016250716679