title: The basis function approach for modeling autocorrelation in ecological data.
abstract: Analyzing ecological data often requires modeling the autocorrelation created by spatial and temporal processes. Many seemingly disparate statistical methods used to account for autocorrelation can be expressed as regression models that include basis functions. Basis functions also enable ecologists to modify a wide range of existing ecological models in order to account for autocorrelation, which can improve inference and predictive accuracy. Furthermore, understanding the properties of basis functions is essential for evaluating the fit of spatial or time-series models, detecting a hidden form of collinearity, and analyzing large data sets. We present important concepts and properties related to basis functions and illustrate several tools and techniques ecologists can use when modeling autocorrelation in ecological data.
authors.affiliation: Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA.|Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Trevor J
authors.initials: TJ
authors.lastname: Hefley
authors.affiliation: Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Kristin M
authors.initials: KM
authors.lastname: Broms
authors.affiliation: Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Brian M
authors.initials: BM
authors.lastname: Brost
authors.affiliation: Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Frances E
authors.initials: FE
authors.lastname: Buderman
authors.affiliation: Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Shannon L
authors.initials: SL
authors.lastname: Kay
authors.affiliation: Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Henry R
authors.initials: HR
authors.lastname: Scharf
authors.affiliation: Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: John R
authors.initials: JR
authors.lastname: Tipton
authors.affiliation: Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA.|Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA.
authors.forename: Perry J
authors.initials: PJ
authors.lastname: Williams
authors.affiliation: Department of Fish, Wildlife, and Conservation Biology, Colorado State University, Fort Collins, Colorado 80523 USA.|Department of Statistics, Colorado State University, Fort Collins, Colorado 80523 USA.|U.S. Geological Survey, Colorado Cooperative Fish and Wildlife Research Unit, Fort Collins, Colorado 80523 USA.
authors.forename: Mevin B
authors.initials: MB
authors.lastname: Hooten
mesh_terms: D004463:Ecology; D008962:Models, Theoretical
keywords: Bayesian model; autocorrelation; collinearity; dimension reduction; semiparametric regression; spatial statistics; time series