Modelling data from different sites, times or studies: Weighted vs. unweighted regression

Abstract

We consider the use of weighted regression when modelling data from different sites, times or studies. Our primary focus is on the coverage rate of the 95% confidence interval for the slope parameter when we have a single predictor variable. We use simulation to assess this coverage rate for both weighted and unweighted regression, across a range of scenarios likely to be encountered in ecology. Our results are surprising: unweighted regression will often be more reliable than weighted regression. The well-known advantages of weighted regression are offset by having to estimate the process error variance. Although unweighted regression involves assuming that the measurement error variances are equal, the coverage rate is remarkably robust to departures from this assumption. Unweighted regression will often be more robust because it does not make use of potentially poor information on the measurement error variances. The only situation in which unweighted regression will perform poorly is when there is a strong relationship between the precision of an estimate and its leverage in the regression. We propose a simple diagnostic tool to assess when this might be the case. The implications of our results are important in a management context as they indicate the benefits obtained from using a simple, readily understood approach to combining information. © 2011 The Authors. Methods in Ecology and Evolution © 2011 British Ecological Society.