[R] Compare two normal to one normal

[John Sorkin]

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 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.