[R] mgcv, testing gamm vs lme, which degrees of freedom?
c.fezzi at uea.ac.uk
Fri Jun 18 16:24:14 CEST 2010
thanks for your reply, sorry I was being sloppy regarding the random
effect representation fo the smooth functions.
I am using the identity link, but I am not sure if the anova command will
work since the df are the same as in Loglik. For example, if you add the
following code to my previous example:
f3 <- gamm(y ~ x + I(x^2), random = list(id=~1), method="ML")
You will see that the number of degree of freedom of model f2 and f3 is
the same. This seems very strange to me, do you think is correct?
> I see this question is still open, so let me try to give you some
> answer. As far as I understood, the smoothing splines are not used as
> pure random effects, but as a combination of random and fixed effects.
> Very simplified, the first two basis functions (intercept and linear
> effect) are added as a fixed effect, whereas all other basis functions
> go to the random component. Hence, the df for the log likelihood will
> be indeed smaller than in the case of gam, where all splines are
> considered fixed effects.
> I've struggled with this issue myself as well, and I still don't
> understand it fully. I believe I have the concepts down by now, but
> the mathematical background requires more study for me I'm afraid. Did
> you read the book of Simon Wood already?
> Simon Wood advises to compare models using the anova's for the
> lme-part of the object, i.e.
> anova(model1$lme, model2$lme).
> where one model contains the smoothing term of interest and the other
> doesn't. I base most of my model testing in the gamm context on these
> tests. To be completely correct, this -apparently- only counts for
> gamms using the identity link.
> On Wed, Jun 16, 2010 at 9:33 PM, Carlo Fezzi <c.fezzi at uea.ac.uk> wrote:
>> Dear all,
>> I am using the "mgcv" package by Simon Wood to estimate an additive
>> model in which I assume normal distribution for the residuals. I would
>> like to test this model vs a standard parametric mixed model, such as
>> ones which are possible to estimate with "lme".
>> Since the smoothing splines can be written as random effects, is it
>> correct to use an (approximate) likelihood ratio test for this? If so,
>> which is the correct number of degrees of freedom? Sometime the function
>> LogLik() seems to provide strange results regarding the number of
>> of freedom (df) for the gam, for instance in the example I copied below
>> the df for the "gamm" are equal to the ones for the "lme", but the
>> summary(model.gam) seems to indicate a much higher edf for the gamm.
>> I would be very grateful to anybody who could point out a solution,
>> Best wishes,
>> Example below:
>> rm(list = ls())
>> x <- runif(100,1,10) # regressor
>> b0 <- rep(rnorm(10,mean=1,sd=2),each=10) # random intercept
>> id <- rep(1:10, each=10) # identifier
>> y <- b0 + x - 0.1 * x^3 + rnorm(100,0,1) # dependent variable
>> f1 <- lme(y ~ x + I(x^2), random = list(id=~1) , method="ML" ) # lme
>> f2 <- gamm(y ~ s(x), random = list(id=~1), method="ML" ) # gamm
>> ## same number of "df" according to logLik:
>> ## much higher edf according to summary:
>> R-help at r-project.org mailing list
>> PLEASE do read the posting guide
>> and provide commented, minimal, self-contained, reproducible code.
> Joris Meys
> Statistical consultant
> Ghent University
> Faculty of Bioscience Engineering
> Department of Applied mathematics, biometrics and process control
> tel : +32 9 264 59 87
> Joris.Meys at Ugent.be
> Disclaimer : http://helpdesk.ugent.be/e-maildisclaimer.php
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