Journal
ECOLOGY
Volume 84, Issue 8, Pages 2034-2041Publisher
ECOLOGICAL SOC AMER
DOI: 10.1890/02-0472
Keywords
bootstrapping; change-point regression; edge effects; forest understory community; (Vancouver Island); piecewise regression; plant community; principal components analysis; segmented regression
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We demonstrate the use of piecewise regression as a statistical technique to model ecological thresholds. Recommended procedures for analysis are illustrated with a case study examining the width of edge effects in two understory plant communities. Piecewise regression models are broken-stick models, where two or more lines are joined at unknown points, called breakpoints. Breakpoints can be used as-estimates of thresholds and are used here to determine the width of edge effects. We compare a sharp-transition model with three models incorporating smooth transitions: the hyperbolic-tangent, benthyperbola, and bent-cable models. We also calculate three types of confidence intervals for the breakpoint estimate: an interval based on the computed standard error of the estimate from the fitting procedure, an empirical bootstrap confidence interval, and a confidence interval derived from an inverted F test. We recommend use of the inverted F test confidence interval when sample sizes are large, and cautious use of bootstrapped confidence intervals when sample sizes are smaller. Our analysis demonstrates the need for a careful study of the likelihood surface when fitting and interpreting the results from piecewise-regression models.
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