[R] Compare two normal to one normal

[John Sorkin]

Bert,Better, perhaps, but will something like the LR test be significant? Adding an extra parameter to a linear regression almost always improves the R2, the if one compares models, the model with the extra parameter is not always significantly better.
John
P.S. Please forgive the appeal to "significantly better" . . .


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) 

>>> Bert Gunter <bgunter.4567 at gmail.com> 09/22/15 4:30 PM >>>
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) 410-605-7119410-605-7119
> (Fax) 410-605-7913 (Please call phone number above prior to faxing)
>
>
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This email message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.