[R] Compare two normal to one normal

[John Sorkin]

I am not sure AIC or BIC would be needed as the two normal distribution has at least two additional parameters to estimate; mean 1, var1, mean 2, var 2 where as the one normal has to estimate only var1 and var2.In any event, I don't know how to fit the single normal and get values for the loglik let alone AIC or BIC
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) 

>>> Mark Leeds <markleeds2 at gmail.com> 09/22/15 4:36 PM >>>
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) 410-605-7119410-605-7119
 > (Fax) 410-605-7913 (Please call phone number above prior to faxing)
 >
 >
 > Confidentiality Statement:
 

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