Confidence Intervals

2 replies [Last post]
MG's picture
MG
Offline
Joined: 10/29/2010

I am a new user of OpenMx , this is my first post.

I am trying to calculate Confidence Intervals on standardized estimates (univariate model). To use the function: mxCI() the standardized estimates have to be defined inside the model.

Does anyone know how to define the standardized estimates within the model so that I can request them in the CI function?

Thanks in advance for your help.

Maria

MG's picture
MG
Offline
Joined: 10/29/2010
Hi Ryne, Thank you for the

Hi Ryne,

Thank you for the detailed instructions!.. this is really of great help! I am trying it out now.

Maria

Ryne's picture
Offline
Joined: 07/31/2009
There are a number of ways to

There are a number of ways to specify standardized solutions. I'll lay out two, and hopefully one will seem most appropriate to you.

Option 1. Don't worry about it! You can always standardize after the fact. Standardization is a linear transformation, so you can just run mxCI on your parameters, then standardize both your parameters and your confidence limits. I wrote a standardizeRAM function (http://openmx.psyc.virginia.edu/thread/718), but you can standardize any model parameter by either (a) dividing it by the product of the model-implied standard deviations of the two variables it relates (for two-headed arrors, i.e., cov_xy/(sd_x * sd_y) = r_xy) or (b) by multiplying by the ratio of model-implied standard deviations (for one headed-arrows, i.e., B_xy * sd_x / sd_y, where x predicts y). Definition variables make life tougher, as you have to remember to standardize them as well.

Option 2. Wrap your model in standard deviations. If you want an actual standardized model, I would take your existing model and do the following things:
-create a diagonal matrix of free parameters. these free parameters will represent the sds of your manifest variables. You may lbound them at zero if you wish.
-change all of the variance parameters in your model to fixed parameters, such that the variance of every variable in your model is 1. Keep in mind that some of the terms in your model are residual variances, and should not themselves be fixed to 1. For instance, if if your entire model is "y regressed on x", fix the variance of x to 1 and the variance of y to be equal to 1-beta^2. Fixing can be done through altering matrices or using mxConstraints and/or mxAlgebras.
-pre- and post-multiply your model expected covariance (which you've now made into a model expected correlation matrix) by your inverse sds matrix.

Obviously option 2 is more involved, but any respecification method will be. Hopefully one of these works out for you.

Edit (11/1/10): Clarified the math in Option 1.