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Behavioral Ecology Advance Access originally published online on November 27, 2008
Behavioral Ecology 2009 20(2):416-420; doi:10.1093/beheco/arn145
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© 2008 The Authors
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Conclusions beyond support: overconfident estimates in mixed models

Holger Schielzeth and Wolfgang Forstmeier

Department of Behavioural Ecology and Evolutionary Genetics, Max Planck Institute for Ornithology, PO Box 1564, 82305 Starnberg (Seewiesen), Germany

Address correspondence to H. Schielzeth. E-mail: schielz{at}orn.mpg.de.


  Abstract

Mixed-effect models are frequently used to control for the nonindependence of data points, for example, when repeated measures from the same individuals are available. The aim of these models is often to estimate fixed effects and to test their significance. This is usually done by including random intercepts, that is, intercepts that are allowed to vary between individuals. The widespread belief is that this controls for all types of pseudoreplication within individuals. Here we show that this is not the case, if the aim is to estimate effects that vary within individuals and individuals differ in their response to these effects. In these cases, random intercept models give overconfident estimates leading to conclusions that are not supported by the data. By allowing individuals to differ in the slopes of their responses, it is possible to account for the nonindependence of data points that pseudoreplicate slope information. Such random slope models give appropriate standard errors and are easily implemented in standard statistical software. Because random slope models are not always used where they are essential, we suspect that many published findings have too narrow confidence intervals and a substantially inflated type I error rate. Besides reducing type I errors, random slope models have the potential to reduce residual variance by accounting for between-individual variation in slopes, which makes it easier to detect treatment effects that are applied between individuals, hence reducing type II errors as well.

Key words: experimental design, maternal effects, mixed-effect models, random regression, repeated measures, type I error.

Received 26 March 2008; revised 27 October 2008; accepted 27 October 2008.


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