*Evol Ecol Res* **16**: 689-704 (2014) Full **PDF** if your library subscribes.

Choice of regression model for isodar analysis Jack W. Bradbury and Sandra L. Vehrencamp

Department of Neurobiology and Behavior, Cornell University, Ithaca, New York, USA

Correspondence: J.W. Bradbury, Department of Neurobiology and Behavior, Cornell University, Ithaca, NY 14853, USA.

e-mail: jwb25@cornell.eduABSTRACT

Background:Isodar analysis allows us to assess the multiple influences of density on relative fitnesses in alternative habitats. It relies on linear regressions. But isodar analyses have a non-classical error structure that complicates the choice of regression method. Prior comparisons of alternative regression methods using simulated data failed to emulate the type of error structure encountered in isodar studies.

Question:Which linear regression method gives the most accurate slope and intercept estimates in isodar analyses?

Method:Simulate datasets that mimic typical isodar studies but have known functional slopes and intercepts, known levels of measurement error, and known equation error. Generate 50 randomly drawn replicates for each combination of input parameters and compare the true slopes to those estimated by each of the four most widely used linear regression methods (ordinary least squares, major axis, geometric mean, and bisected angle protocols). Identify the most reliable method for isodar analyses.

Range of key variables:In total, 14,256 combinations of parameters were examined. Parameter ranges were: mean number ofXYpairs/dataset (20–640), coefficient of variation around mean numbers (5–40%), true slopes (0.5–2.0), ratio of ideal free distributionYmean toXmean (1.2, 1.4), equation error (1–20%), and measurement error (0.1–10%).

Results:All four methods exhibited biases. Bias declined as the Pearson correlation betweenXandYincreased. Ordinary least squares always underestimated true slopes, often severely. The geometric mean and bisected angle protocols underestimated true slopes greater than one, and overestimated those less than one. Major axis regressions showed the reverse pattern of biases and could behave erratically. All four methods gave unreliable slope estimates for Pearson correlation coefficients less than 0.4. For Pearson correlations above that threshold, the geometric mean method had the least bias and remains the most conservative choice for isodar studies.

Keywords: equation error, isodars, measurement error, Model II regression.DOWNLOAD A FREE, FULL PDF COPY

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© 2015 Jack W. Bradbury. All

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