Avoiding Data Snooping in Multilevel and Mixed Effects Models
AbstractMultilevel or mixed effects models are commonly applied to hierarchical data; for example, see Goldstein (2003), Raudenbush and Bryk (2002), and Laird and Ware (1982). Although there exist many outputs from such an analysis, the level-2 residuals, otherwise known as random effects, are often of both substantive and diagnostic interest. Substantively, they are frequently used for institutional comparisons or rankings. Diagnostically, they are used to assess the model assumptions at the group level. Current inference on the level-2 residuals, however, typically does not account for data snooping, that is, for the harmful effects of carrying out a multitude of hypothesis tests at the same time. We provide a very general framework that encompasses both of the following inference problems: (1) Inference on the `absolute' level-2 residuals to determine which are significantly different from zero, and (2) Inference on any prespecified number of pairwise comparisons. Thus, the user has the choice of testing the comparisons of interest. As our methods are flexible with respect to the estimation method invoked, the user may choose the desired estimation method accordingly. We demonstrate the methods with the London Education Authority data used by Rasbash et al. (2004), the Wafer data used by Pinheiro and Bates (2000), and the NELS data used by Afshartous and de Leeuw (2004).
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Bibliographic InfoPaper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 260.
Date of creation: Dec 2005
Date of revision:
Data snooping; hierarchical linear models; hypothesis testing; pairwise comparisons; random e®ects; rankings;
Other versions of this item:
- David Afshartous & Michael Wolf, 2007. "Avoiding 'data snooping' in multilevel and mixed effects models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 1035-1059.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
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- Joseph P. Romano & Michael Wolf, 2003.
"Stepwise Multiple Testing as Formalized Data Snooping,"
17, Barcelona Graduate School of Economics.
- Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, 07.
- Joseph P. Romano & Michael Wolf, 2003. "Stepwise multiple testing as formalized data snooping," Economics Working Papers 712, Department of Economics and Business, Universitat Pompeu Fabra.
- James R. Carpenter & Harvey Goldstein & Jon Rasbash, 2003. "A novel bootstrap procedure for assessing the relationship between class size and achievement," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 431-443.
- Afshartous, David & Preston, Richard A., 2010. "Confidence intervals for dependent data: Equating non-overlap with statistical significance," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2296-2305, October.
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