Avoiding Data Snooping in Multilevel and Mixed Effects Models
Multilevel 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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- Joseph P. Romano & Michael Wolf, 2005.
"Stepwise Multiple Testing as Formalized Data Snooping,"
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.
- Joseph P. Romano & Michael Wolf, 2003. "Stepwise Multiple Testing as Formalized Data Snooping," Working Papers 17, Barcelona Graduate School of Economics.
- Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
- 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.
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