## Obtaining Standard Errors

3 replies [Last post]
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Joined: 03/01/2010

Hi,

I have been able to obtain standard errors for my path estimates by simply using a statement such as:
ACEmodelSumm <- summary(ACEmodelFit)

However, I would like to obtain standard errors for additional parameters, such as genetic correlations and standardized A,C,E estimates (or even simple phenotypic correlations).

Thank you,
Jarrod

(apologies if this has been covered elsewhere)

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Joined: 09/07/2010
You may try the delta method,

You may try the delta method, which is available on wikipedia.

It would also be good to transform the parameter of interest to a scale that is unbounded, b/c usually asymptotic normality requires smaller sample sizes for such transformation.

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Joined: 07/31/2009
Thanks, Mike, for the bump.

Thanks, Mike, for the bump. There are a number of issues with what you're discussing, Jarrod.

First, you should consider mxCI as a way to generate likelihood based confidence intervals. See the following thread regarding this issue (http://openmx.psyc.virginia.edu/thread/536), especially the second portion of the thread that begins with rabil's comments about confidence intervals on algebras.

There's are issues with standard errors for things like the genetic component variances. The meaning of the word 'parameter' is very important. OpenMx provides standard errors for estimated free parameters in the model. If you linearly transform a parameter, then you can similarly transform the SE (i.e., standardization. If you non-linearly transform a parameter (say, by squaring it, or multiplying two parameters together), then you cannot simultaneously assume that the sampling distribution of a parameter and its non-linear transformation are both symmetric around the parameter.

For example, consider an estimated standard deviation of 2 with a standard deviation of 1. Based on normal theory, we should have 95% confidence that the actual value of that SD in the population is 2 plus or minus 1.96*1 (Confidence interval of 0.04 to 3.96). Were we to square that term, we'd get a variance of 4, but we cannot assume the standard deviation is 1^2: were we to square the previous CI, we'd get a confidence interval of 0.0016 to 15.6816, which is decidedly non-symmetric around 4.

As I've rambled for a while, I'll again push you towards mxCI for generating confidence intervals for parameters and their algebraic transformations, and urge you to specify your models using the parameters you want (phenotypic correlations and genetic component variances) if you really want standard errors.

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Joined: 07/31/2009
Bump. Someone should post an

Bump. Someone should post an answer. I think the reply will have something to do with calculating confidence intervals, but this is not really my area so I'm going to leave it to others.