# [R] mgcv, testing gamm vs lme, which degrees of freedom?

Carlo Fezzi c.fezzi at uea.ac.uk
Fri Jun 18 16:24:14 CEST 2010

```Hi Joris,

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")
anova(f3\$lme,f2\$lme)

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?

Best wishes,

Carlo

> 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
>
>
> 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.
>
> Cheers
> Joris
>
> 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
>> mixed
>> 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
>> the
>> 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
>> degrees
>> 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,
>>
>> Carlo
>>
>> Example below:
>>
>> ----
>>
>> rm(list = ls())
>> library(mgcv)
>> library(nlme)
>>
>> set.seed(123)
>>
>> 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
>> model
>>
>> f2 <- gamm(y ~ s(x), random = list(id=~1), method="ML" )    # gamm
>>
>> ## same number of "df" according to logLik:
>> logLik(f1)
>> logLik(f2\$lme)
>>
>> ## much higher edf according to summary:
>> summary(f2\$gam)
>>
>> -----------
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> 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
>

```