A nonparametric bootstrap for multilevel models

Bootstrapping is now a well established procedure for assessing the bias and standard error of parameters in statistical models (Davison and Hinckley, 1997). Given a fitted model and parameter estimates, the idea is to generate synthetic (termed bootstrap) data from the fitted model, and then refit the model to the synthetic data, thus obtaining a set of synthetic (termed bootstrap) parameter estimates. These synthetic parameter estimates stand in approximately the same relationship to the model parameter estimates as the model parameter estimates stand in relationship to the population parameters. Thus, we can estimate quantities of interest relating the population parameters and the estimated parameters (such as bias, confidence intervals) by looking at the relationship between the estimated parameters and the synthetic, or bootstrap, parameters.

[1]  MULTILEVEL MODELLING NEWSLETTER , 1995 .

[2]  K. Jones,et al.  Department size and research in English Universities: inter-university variations , 1995 .

[3]  E. Oord,et al.  An examination of genotype-environment interactions for academic achievement in an U.S. national , 1997 .

[4]  Michael P. Cohen,et al.  Outmigration Among Rural High School Graduates: The Effect of Academic and Vocational Programs , 1997 .

[5]  E. Fieldhouse,et al.  Using the 1991 Census SAR in a Multilevel Analysis of Male Unemployment , 1997, Environment & planning A.

[6]  G. Moon,et al.  Guest editorial: the scope of multilevel models , 1997 .

[7]  Clive R. Belfield,et al.  The Consequences of Drop‐outs on the Cost‐effectiveness of 16‐19 Colleges , 1998 .

[8]  E. Fieldhouse,et al.  Ethnic Minority Unemployment and Local Labour Market Conditions in Great Britain , 1998, Environment & planning A.

[9]  D. Hedeker,et al.  A Multilevel Thresholds of Change Model for Analysis of Stages of Change Data , 1998 .

[10]  Michael P. Cohen.  Determining sample size for surveys with data analyzed by hierarchical linear models , 1998 .

[11]  Daniel B. Wright,et al.  Modelling Clustered Data in Autobiographical Memory Research: The Multilevel Approach , 1998 .

[12]  A. Fielding.  Perspectives on Performance Indicators: GCE Advanced Level and Differences Between Institution Types in Cost Effectiveness∗ , 1998 .

[13]  J. Lindsey,et al.  Some statistical heresies , 1999 .

[14]  Harvey Goldstein,et al.  The use of assessment data for school improvement purposes , 1999 .

[15]  M. Hardy,et al.  A Multilevel Model of Early Retirement Decisions among Autoworkers in Plants with Different Futures , 1999 .

[16]  Debashis Kushary,et al.  Bootstrap Methods and Their Application , 2000, Technometrics.

[17]  Neil Spencer,et al.  A Comparison of Modelling Strategies for Value-Added Analyses of Educational Data , 2002, Comput. Stat..