Non‐parametric habitat models with automatic interactions

Abstract

Questions: Can a statistical model be designed to represent more directly the nature of organismal response to multiple interacting factors? Can multiplicative kernel smoothers be used for this purpose? What advantages does this approach have over more traditional habitat modelling methods? Methods: Non‐parametric multiplicative regression (NPMR) was developed from the premises that: the response variable has a minimum of zero and a physiologically‐determined maximum, species respond simultaneously to multiple ecological factors, the response to any one factor is conditioned by the values of other factors, and that if any of the factors is intolerable then the response is zero. Key features of NPMR are interactive effects of predictors, no need to specify an overall model form in advance, and built‐in controls on overfitting. The effectiveness of the method is demonstrated with simulated and real data sets. Results: Empirical and theoretical relationships of species response to multiple interacting predictors can be represented effectively by multiplicative kernel smoothers. NPMR allows us to abandon simplistic assumptions about overall model form, while embracing the ecological truism that habitat factors interact.

Interactions between macroinvertebrate taxa and complex environmental gradients influencing abundance and distribution in the Umatilla River, Northeastern Oregon

“…For this analysis, the observed environmental variables at each data point are adjusted by a small amount and the resultant change in the estimated response value was indicative of the impact of that environmental variable on the model. A value of 1.0 indicates a change in the response equal in magnitude to the change in the environmental variable, and a value of 0.0 indicates no change in the response with change in the environmental variable (McCune 2006).…”

“…A local mean estimator with Gaussian weighting was used in a forward step-wise regression, and a method of cross-validated R 2 (xR 2 ) was implemented to evaluate fit of the model and to prevent over-fitting. Evaluating the model using xR 2 is a 'leave-one-out' approach, excluding a data point in the calculation of the response (McCune 2006).…”

“…There have also been applications of NPMR in the plant sciences (McCune et al 2003;Antoine and McCune 2004;Ellis and Coppins 2007;Wellstein et al 2007), river ecology (Miller 2007), and in government agency reporting (Vander Haegen et al 2004). NPMR avoids the requirement of pre-specified responses inherent in linear and logistic regression models and incorporates a non-parametric smoothing technique, which makes modeling interactions among predictors much more parsimonious than in traditional mathematical models (McCune 2006).…”

Physiologically derived predictions of Douglas-fir site index in British Columbia

“…glas-fir stands within BEC subzones we utilized a species prediction model for Douglas-fir based on climate attributes developed using nonparametric regression (McCune 2006). The approach produced spatial predictions of the percent likelihood of the presence of Douglas-fir at 1-km spatial resolution across the Province (see Schroeder et al 2009a for more details on the modelling approach and accuracy).…”

Hydroecological model predictions indicate wetter and more diverse soil water regimes and vegetation types following floodplain restoration

“…[16] Goodness of fit for the non-parametric regression models was determined using a cross-validated log likelihood ratio (logb), which quantifies model improvement over a naïve model that estimates the probability of presence to be uniform and equal to the overall frequency in the data set [McCune, 2006]. Jeffreys [1935] and Yost [2008] suggest the following interpretation of logb values: 0-0.5, weak; 0.5-1, substantial; 1-2, strong; >2, decisive.…”