# Nonlinear transformation and estimates

4 posts / 0 new
Offline
Joined: 03/29/2012 - 09:40
Nonlinear transformation and estimates

Hi. I have a question about analysis of non-linear transformed variables. I have a continuous variable which is skewed (1.2). Box-Cox transformation suggested 1/y transformation. If I run ACE models (and saturated) on this new variables, how do I interpret and report the results? Is it common to report the estimates for the transformed variable? And is it possible to get the estimates for the original raw variable then?
Julia

Offline
Joined: 01/24/2014 - 12:15
transformation
If I run ACE models (and saturated) on this new variables, how do I interpret and report the results?

They'd be in the units of the transformed variable. For instance, suppose your original variable was body mass in kg. Then, the mean you estimate for the transformed variable would be in kg^-1, and the variance would be in kg^-2.

Is it common to report the estimates for the transformed variable?

Yes. Just make sure your reader/audience knows that you've analyzed the transformed variable, not the raw variable.

And is it possible to get the estimates for the original raw variable then?

Only if you know or assume an explicit distribution for the original variable.

If you're concerned about the skewness of the original variable biasing your statistical inferences (confidence intervals and hypothesis tests), then instead of transforming the variable, you could leave analyze it untransformed and carryout nonparametric inference, like bootstrapping.

Offline
Joined: 03/29/2012 - 09:40

So the bootstrapping would solve the problem of confidence intervals? This is great! But what about the hypothesis testing? How would bootstrapping come into a picture here? Would I have to run bootstrapping of every submodel?

Thank you again for your help!

Offline
Joined: 01/24/2014 - 12:15
hypothesis testing

Obviously, for single-parameter inference conditional on some model, bootstrap CIs will give you an interval of parameter values you would retain if you used them as null parameter values in a hypothesis test.

As for multiparameter inference or model comparison, I'm afraid OpenMx does not currently have any built-in features useful for those purposes.

Edit: actually, I guess maybe you could calculate robust standard errors and do a multiparameter Wald test. And if you pass details=TRUE to imxRobustSE(), you can get the model's Takeuchi Information Criterion (TIC), which is a generalization of AIC that relies upon fewer assumptions.