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

[Spencer Graves]

	  Have you considered 'simulate.lme'?  I believe that this is what 
Bates included in the 'nlme' package for obtaining confidence intervals, 
joint confidence regions, etc., when there were questions about the 
results for whatever reason.  I have not tried it with a singular model, 
but I believe Bates has.  In particular, have you reviewed ch. 2 in 
Pinheiro and Bates (2000) Mixed-Effects Models in S and S-Plus (Springer)?

	  I am not a fan of bootstrapping.  In mixed-effects applications, 
bootsrapping needs to incorporate the constraints imposed by the 
mixed-effects model.  For example, if you have several samples per batch 
and several batches per lot, you need to bootstrap lots as well as 
batches within lot and samples within batch.

	  The advantage of bootstrapping is that if the normality assumptions 
behind the mixed model do not hold, the bootstrap results will still 
have some validity.  However, the range of extrapolability of bootstrap 
results is limited to other situations whose distribution is plausibly 
like the particular sample you bootstrapped, and I wouldn't know how to 
evaluate that.  By contrast, I know how to extrapolate simulation 
results.  To decide whether such results apply, I make normal 
probability plots of the data, random effects, and residuals.  If they 
all seem normal, I feel it is reasonable to use the simulation results.

	  Others may offer a different perspective (or a correction, as the 
case may be).  However, you asked for comments about bootstrapping mixed 
models.  At least you've got one.

	  Hope this helps.
	  Spencer Graves

Bruno L. Giordano wrote:
> 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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