# [R] Compare two normal to one normal

Bert Gunter bgunter.4567 at gmail.com
Tue Sep 22 22:30:34 CEST 2015

```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
>
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>
> 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)
>
>
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