[R] Compare two normal to one normal

John Sorkin
2015-09-22T20:21:36Z

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
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