Hi.

Is it possible to get bootstrap confidence intervals for algebras? I am running a trivariate CHolesky decomposition model on binary variables and estimating CI's through mxCI takes more than 24h. When I ran mxBoostrap, I got CI's only for model parameters, but not for algebras. Is there a way to specify it? Or is there a way to reduce the time to running a model with intervals=T?

Thank you in advance!

Julia

Hi Julia

I don't think there's anything built-in, but in principle you could take the bootstrap estimates, one line (i.e. one set of parameter estimates) at a time, and use omxSetParameters to update the model, then use mxEval to obtain the algebras of interest.

However, it might be easier not to use the Cholesky and to simply estimate A C and E matrices as symmetric matrices. This might give you quantities closer to what interests you (and avoid some statistical issues with the Cholesky).

Your likelihood-based CIs seem extra slow - perhaps ordinal data in an ordinal model. See also mxSE() which can now produce standard errors for algebras. Much faster and not too different from likelihood-based CIs if the asymptotic behavior has been attained.

Cheers

Mike

Works like mxEval but for bootstrap

Thanks a lot! I think this is what I needed!

Thank you, Mike, for a prompt reply! mxSE() are not working with my model as I have mxConstraint in the script to constrain the variance if the binary variable to 1. Estimating A,C and E matrices instead sounds like a good idea. Although I have a question about setting lower boundaries for diagonal elements which are variances. Nowhere in the Boulder scripts I found that those were constrained to be non-negative. Is there a reason for that?

When I let them be estimated without boundaries, I get negative variances. When I constrain only diagonal elements to be greater than or equal to zero, I get negative covariances which was not the case when I ran the classical Cholesky script. At the same time I don't feel comfortable with forcing covariances to be non-negative. Could you please advise?

Several reasons, in fact:

A,C,Ecovariance matrices don't have to be PD; only the phenotypic covariance matrix does.A,C,Ecovariance matrices are all PD, the phenotypic covariance matrix will necessarily be also. In the past, using that fact to ensure a PD phenotypic covariance matrix at all times may have been necessary for optimization. But, it isn't anymore.All of OpenMx's optimizers with which I'm familiar (the 3 main ones and 2 niche ones) are all able to recover if they step outside the parameter space.

The main reason:when one or more parameter estimates is on or near an "artificial" bound, likelihood-ratio test statistics concerning those parameters will not have their theoretical chi-square null distribution. Since MxCIs invert the LRT, it is also true that they will not have their desired repeated-sampling coverage probability when point estimates are on or near a bound.