# [R] Compare two normal to one normal

Mark Leeds markleeds2 at gmail.com
Tue Sep 22 22:35:56 CEST 2015

```That's true but if he uses some AIC or BIC criterion that penalizes the
number of parameters,
then he might see something else ? This ( comparing mixtures to not
mixtures ) is not something I deal with so I'm just throwing it out there.

On Tue, Sep 22, 2015 at 4:30 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:

> Two normals will **always** be a better fit than one, as the latter
> must be a subset of the former (with identical parameters for both
> normals).
>
> Cheers,
> Bert
>
>
> Bert Gunter
>
> "Data is not information. Information is not knowledge. And knowledge
> is certainly not wisdom."
>    -- Clifford Stoll
>
>
> On Tue, Sep 22, 2015 at 1:21 PM, John Sorkin
> <JSorkin at grecc.umaryland.edu> wrote:
> > I have data that may be the mixture of two normal distributions (one
> contained within the other) vs. a single normal.
> > I used normalmixEM to get estimates of parameters assuming two normals:
> >
> >
> > GLUT <- scale(na.omit(data[,"FCW_glut"]))
> > GLUT
> > mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE)
> > summary(mixmdl)
> > plot(mixmdl,which=2)
> > lines(density(data[,"GLUT"]), lty=2, lwd=2)
> >
> >
> >
> >
> >
> > summary of normalmixEM object:
> >            comp 1   comp 2
> > lambda  0.7035179 0.296482
> > mu     -0.0592302 0.140545
> > sigma   1.1271620 0.536076
> > loglik at estimate:  -110.8037
> >
> >
> >
> > I would like to see if the two normal distributions are a better fit
> that one normal. I have two problems
> > (1) normalmixEM does not seem to what to fit a single normal (even if I
> address the error message produced):
> >
> >
> >> mixmdl = normalmixEM(GLUT,k=1)
> > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k =
> k,  :
> >   arbmean and arbvar cannot both be FALSE
> >> mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE)
> > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k =
> k,  :
> >   arbmean and arbvar cannot both be FALSE
> >
> >
> >
> > (2) Even if I had the loglik from a single normal, I am not sure how
> many DFs to use when computing the -2LL ratio test.
> >
> >
> > Any suggestions for comparing the two-normal vs. one normal distribution
> would be appreciated.
> >
> >
> > Thanks
> > John
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > John David Sorkin M.D., Ph.D.
> > Professor of Medicine
> > Chief, Biostatistics and Informatics
> > University of Maryland School of Medicine Division of Gerontology and
> Geriatric Medicine
> > Baltimore VA Medical Center
> > 10 North Greene Street
> > GRECC (BT/18/GR)
> > Baltimore, MD 21201-1524
> > (Phone) 410-605-7119
> > (Fax) 410-605-7913 (Please call phone number above prior to faxing)
> >
> >
> > Confidentiality Statement:
> > This email message, including any attachments, is for ...{{dropped:12}}
>
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