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Re: st: Mixed effects model for asymmetric data


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Mixed effects model for asymmetric data
Date   Wed, 26 Sep 2012 14:38:38 -0400

On Wed, Sep 26, 2012 at 2:15 PM, Ana Beatriz FS
<nutrianabeatriz@gmail.com> wrote:
> Thanks,  JVVerkuilen,
>
> Unfortunately my variable is not a count one, I work with levels of hormones.

Ah.


> Following your suggestion, I assessed the quality of the model by the
> residuals and it's really really bad.
>
> With respect to the transformations, they produce quite different
> distributions. I haven't find one that would fit all my points in
> time, even if not perfectly. I do think I have a problem here!

So what are the various transformations you're getting? I assume
you're fitting Box-Cox models within a time point, or something like
that? If most of the Box-Cox parameters are between 0 and 0.5, you
might simply have to deal with picking a reasonable compromise value,
though I suppose a rather complicated nonlinear model that took
transformation into account over time could be made (but wow...). How
are you measuring your distributions' differences? You might want to
pick a reasonable and interpretable compromise transformation, use it
and then assess the residuals.

I have found that the inverse hyperbolic sine is frequently overlooked
and often useful. It's a rather nice compromise between log and sqrt
that is well-defined for values of 0. There's a small literature on
it, with two citations given below.

     -generate IHSmyvar = asinh(myvar)-

Layton, David F, 2001. "Alternative Approaches for Modeling
Concave Willingness to Pay Functions in Conjoint Valuation,"
American Journal of Agricultural Economics, vol. 83(5), 1314-20.

Burbidge, John B., Lonnie Magee and A. Leslie Robb. 1988 "Alternative
Transformations to Handle Extreme Values of the Dependent Variable."
Journal of the American Statistical Association, vol. 83, 123-127.


-- 
JVVerkuilen, PhD
jvverkuilen@gmail.com

"Out beyond ideas of wrong-doing and right-doing there is a field.
I'll meet you there. When the soul lies down in that grass the world
is too full to talk about." ---Rumi
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