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RE: st: REML with non-normally distributed dependent Variable


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: REML with non-normally distributed dependent Variable
Date   Wed, 3 Jun 2009 15:50:50 +0100

Maximum likelihood is a general procedure which is in no sense _assumes_
multivariate normality. It is the other way round: a researcher
specifies the distribution or set-up that applies, and then applies ML
if so wished. ML as a principle or method is independent of the
distributions that may be specified.  

But you are talking about REML which although a popular label does not
encapsulate all the assumptions that may be made under its name.  

If you are correct about the particular model you have in mind, you will
be able to find a textbook statement of the fact. What I am clear is
that there are many myths that normality is required for this and that
method, which are commonly believed, regardless of the lack of
foundation. 

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

Christian Weiss

as initially mentioned I am using the variable as dependent variable
for a random intercept model estimaed with REML (using xtmixed).
Afaik univariate normal-distribution is one of the prerequesits for
multivariate normality which is one of the assumptions for ML
estimators?!

On Wed, Jun 3, 2009 at 4:19 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:

> In absolute terms the fit looks pretty lousy to me! However, that may
> not matter at all. You are looking at the marginal distribution of the
> response. Where does it say that matters for that what you have in
mind?

Christian Weiss

> Thank you for your answer!
>
> I already log-transformed the variable, yielding the following result:
>
> http://yfrog.com/11graphpp
>
> ...looks relatively normally distributed to me.
>
> Unfortunately, swilk and swfrancia still tell me that it's not
> normally distributed...
>
> On Tue, Jun 2, 2009 at 10:04 PM, Dan MacNulty <macn0007@umn.edu>
wrote:
>> Why not transform your dependent variable (e.g, log-transform) to
>> approximate a normal distribution? Dan
>>
>> Christian Weiss wrote:
>
>>> I am working with a random-intercept model using REML. As it turned
>>> out my dependent variable is not normally distributed.
>>> If I recall it correctly, one of the assumptions of ML is
> multivariate
>>> normality. Do you have any advice what to do or to consider?

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