[R] non positive-definite G matrix in mixed models: bootstrap?

Doran, Harold HDoran at air.org
Tue Jul 11 16:23:46 CEST 2006

There is a paper by Rogosa and Saner which shows some equivalences in
what you are doing under certain conditions. They show similarities
between bootstrapping with linear models and how the estimates might be
similar to those obtained from a mixed model.

Rogosa, D. R., and Saner, H. M. (1995). Longitudinal data analysis
examples with random coefficient models. 
Journal of Educational and Behavioral Statistics, 20, 149-170. 


> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch 
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bruno 
> L. Giordano
> Sent: Tuesday, July 11, 2006 9:31 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] non positive-definite G matrix in mixed models: 
> bootstrap?
> Dear list,
> In a mixed model I selected I find a non positive definite 
> random effects variance-covariance matrix G, where some 
> parameters are estimated close to zero, and related 
> confidence intervals are incredibly large.
> Since simplification of the random portion is not an option, 
> for both interest in the parameters and significant increase 
> in the model fit, I would like to collect "unbiased" random 
> effects estimates.
> I used bootstrap to this purpose, creating a linear model for 
> each cluster and bootstraping the variance of the 
> coefficients. Is this procedure reasonable? Would it be 
> reasonable in this case to keep the marginal portion of the 
> mixed model?
> Note that in presence of positive-definite G matrix this 
> bootstrap approach and the mixed effect model give highly 
> similar estimates and that in the non positive-definite model 
> the bootstrap and mixed model marginal-model estimates are 
> highly similar as well.
> Thank you
>     Bruno
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