On Tue, 22 Sep 2015, John Sorkin wrote:
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.
Well you *did* ask how to calculate the log-likelihood of a fitted normal density, didn't you? That is what I responded to. You can check that result longhand as sum( dnorm( y, y.mean, y.std , log=TRUE ) ) and get the same result (as long as you used ML estimates of the mean and standard deviation).
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?
As Rolf points out there is a literature on such tests (and Googling 'test finite mixture' covers much of it).
Do you really want a test? If you merely want to pick a winner from two candidate models there are other procedures. k-fold crossvalidation of the loglikelihood ratio statistic seems like an easy, natural approach.
HTH, Chuck ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
