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# st: RE: RE: effect size in nonlinear regression

 From Nick Cox To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: RE: effect size in nonlinear regression Date Tue, 16 Nov 2010 17:51:37 +0000

```There seems to be some latent LaTeX lingering in your equation, but I guess that your curve shifts will not easily reduce to single numbers. I think you need graphs rather than global measures.

Nick
n.j.cox@durham.ac.uk

Airey, David C

I appreciate the replies, and sorry for not being clear.

Were I talking about a power analysis for the t-test and effect sizes,
I might talk in terms of Cohen's d, or (mean1 - mean2)/s, because I
have to capture the mean difference and the variation in the groups.

I was looking into power analysis of a 4 parameter log-logistic equation,

f(x) = c + frac{d-c}{1+exp(b(log(x)-log(e)))}

and was wondering about comparable effect size measures between two curves for
a difference in one of the parameters, that also captures the guassian variation around
the curves and the difference in the parameter.

> I don't know what you mean precisely by effect size. I can guess, but I do not know.
>
> But I see no problem in using R^2, meaning square of correlation between observed and predicted, as a descriptive measure for nonlinear regression. That does not rule out other interpretations for R^2 defined in other ways. This viewpoint is developed at
>
> FAQ     . . . . . . . . . . . . . . . . . . . . . . . Do-it-yourself R-squared
>         . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N. J. Cox
>         9/03    How can I get an R-squared value when a Stata command
>                 does not supply one?
>
> http://www.stata.com/support/faqs/stat/rsquared.html
>
>
> It is arguable that much confusion has arisen because in simple linear models various different viewpoints all produce the same algebra. It may be you are focusing on nonlinearity when the bigger problems of interpretation often arise from non-additivity.
>
> Also, even people who should know better can be too attracted by the idea of summarizing model merit by single figures of merit. Me too, some of the time.
>
> Nick
> n.j.cox@durham.ac.uk

> In linear regression or ANOVA, effect size can be eta^2 or omega^2, the amount of explained variation in the sample or population, respectively. Do these concepts translate to nonlinear regression? Does anyone have any favorite references discussing statistical power and effect size measures for nonlinear regression? I'm guessing these concepts don't translate to nonlinear regression, because I see some cautions about interpreting R^2 in nonlinear regression. I'm trying to understand how one expresses a change in a nonlinear regression parameter in terms of some kind of standardized effect size.
>

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