# Nonlinear transformation and estimates

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Julia
Joined: 03/29/2012

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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?

Thank you in advance!

Julia

Thank you in advance!

Julia

## transformation

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.

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

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.

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## Thank you for the answer!

Thank you again for your help!

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In reply to Thank you for the answer! by Julia

## hypothesis testing

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.

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