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st: Nonparametric multilevel residuals bootstrapping in Stata?


From   Jordan Silberman <[email protected]>
To   [email protected]
Subject   st: Nonparametric multilevel residuals bootstrapping in Stata?
Date   Thu, 18 Jul 2013 16:32:30 -0400

Hi,

I'd like to bootstrap a multilevel model using nonparametric residuals
bootstrapping (aka "semiparametric bootstrapping"). The idea is that
you compute the multilevel model using xtmixed or something similar
and compute residuals at each level of the model. For each bootstrap
iteration you compute new values of the DV by multiplying values of
fixed effect predictors by the appropriate coefficients and then
adding a residual from each level. These residuals are randomly
sampled (with replacement) from the observed residuals. Then you run
the model with the resultant values of the outcome variable specified
as the DV.

The problem with this approach is that the residuals computed by the
multilevel model are shrunk toward unit-specific means--they
underestimate the magnitude of the residuals you'd expect to observe
in a new sample from the population. So, the residuals must be
"unshrunk." In the article pasted below, Carpenter et al. (2003)
present a method for doing this that "unshrinks" the residuals and
also reproduces the appropriate covariance structure of the residuals.

Does anyone know if there's a relatively simple way of reproducing
this procedure in Stata? MLwiN can do it, but I'd like to be able to
do it in Stata.

Thanks!
Jordan

Carpenter, J.R., Goldstein, H., and Rasbah, J. (2003), “A novel
bootstrap procedure for assessing the relationship between class size
and achievement.” Appl. Statist. , Vol. 52, pp 431-443

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