# [R] Compare two normal to one normal

John Sorkin JSorkin at grecc.umaryland.edu
Wed Sep 23 03:39:43 CEST 2015

```Charles,
I am not sure the answer to me question, given a dataset, how can one compare the fit of a model of the fits the data to a mixture of two normal distributions to the fit of a model that uses a single normal distribution, can be based on the glm model you suggest.

I have used normalmixEM to fit the data to a mixture of two normal curves. The model estimates four (perhaps five) parameters: mu1, sd^2 1, mu2, sd^2, (and perhaps lambda, the mixing proportion. The mixing proportion may not need to be estimated, it may be determined once once specifies mu1, sd^2 1, mu2, and sd^2.) Your model fits the data to a model that contains only the mean, and estimates 2 parameters mu0 and sd0^2.  I am not sure that your model and mine can be considered to be nested. If I am correct I can't compare the log likelihood values from the two models. I  may be wrong. If I am, I should be able to perform a log likelihood test with 2 (or 3, I am not sure which) DFs. Are you suggesting the models are nested? If so, should I use 3 or 2 DFs?

May 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)

>>> "Charles C. Berry" <ccberry at ucsd.edu> 09/22/15 6:23 PM >>>
On Tue, 22 Sep 2015, John Sorkin wrote:

>
> In any event, I still don't know how to fit a single normal distribution
> and get a measure of fit e.g. log likelihood.
>

Gotta love R:

> y <- rnorm(10)
> logLik(glm(y~1))
'log Lik.' -17.36071 (df=2)

HTH,

Chuck

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.
```