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

From: Bruno L. Giordano <bruno.giordano_at_music.mcgill.ca>
Date: Tue 11 Jul 2006 - 23:31:29 EST


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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