I would be very nervous about relying on an anova call here. It will
attempt a generalized likelihood ratio test, but gamm is using penalized
quasi likelihood and there is really no likelihood here (even without
the problem that if there was a likelihood the null hypothesis would
still be on the edge of the feasible parameter space making the GLRT
problematic). The best hope might be to model the random effect of xc
using a term s(xc,bs="re") in the model formula (xc will need to be a
factor for this), and then use summary on the gam part of the fitted
model object to assess significance. If you do this you'll need to
include the grouping factor explicitly in corAR1 (at present it's picked
up from the random effect, so is nested in xc).
i.e
g2 <- gamm(y ~ s(xc) +z+ int,family=binomial, weights=trial, random =
list(xc=~1),correlation=corAR1())
becomes something like...
xf <- factor(xc)
g2 <- gamm(y ~ s(xc) +z+ int + s(xf,bs="re"),family=binomial,
weights=trial,
correlation=corAR1(form=~1|xf))
summary(g2$gam)
... I'm also a bit nervous about xc entering as an iid random effect and
the argument of a smooth, however - does that model structure really
make sense?
best,
Simon
On 11/06/13 18:08, William Shadish wrote:
Gavin et al.,
Thanks so much for the help. Unfortunately, the command
> anova(g1$lme, g2$lme)
gives "Error in eval(expr, envir, enclos) : object 'fixed' not found
and for bam (which is the one that can use a known ar1 term), the
error is
> AR1 parameter rho unused with generalized model
Apparently it cannot run for binomial distributions, and presumably
also Poisson.
I did find a Frequently Asked Questions for package mgcv page that said
"How can I compare gamm models? In the identity link normal errors
case, then AIC and hypotheis testing based methods are fine. Otherwise
it is best to work out a strategy based on the summary.gam"
So putting all this together, I take it that my binomial example will
not support a direct model comparison to test the significance of the
random effects. I'm guessing the best strategy based on the
summary.gam is probably just to compare fit indices like Log Likelihoods.
If anyone has any other suggestions, though, please do let me know.
Thanks so much.
Will Shadish
On 6/7/2013 3:02 PM, Gavin Simpson wrote:
On Fri, 2013-06-07 at 13:12 -0700, William Shadish wrote:
Dear R-helpers,
I'd like to understand how to test the statistical significance of a
random effect in gamm. I am using gamm because I want to test a model
with an AR(1) error structure, and it is my understanding neither gam
nor gamm4 will do the latter.
gamm4() can't yes and out of the box mgcv::gam can't either but
see ?magic for an example of correlated errors and how the fits can be
manipulated to take the AR(1) (or any structure really as far as I can
tell) into account.
You might like to look at mgcv::bam() which allows an known AR(1) term
but do check that it does what you think; with a random effect spline
I'm not at all certain that it will nest the AR(1) in the random effect
level.
<snip />
Consider, for example, two models, both with AR(1) but one allowing a
random effect on xc:
g1 <- gamm(y ~ s(xc) +z+ int,family=binomial, weights=trial,
correlation=corAR1())
g2 <- gamm(y ~ s(xc) +z+ int,family=binomial, weights=trial, random =
list(xc=~1),correlation=corAR1())
Shouldn't you specify how the AR(1) is nested in the hierarchy here,
i.e. AR(1) within xc? maybe I'm not following your data structure
correctly.
I include the output for g1 and g2 below, but the question is how to
test the significance of the random effect on xc. I considered a test
comparing the Log-Likelihoods, but have no idea what the degrees of
freedom would be given that s(xc) is smoothed. I also tried:
anova(g1$gam, g2$gam)
gamm() fits via the lme() function of package nlme. To do what you want,
you need the anova() method for objects of class "lme", e.g.
anova(g1$lme, g2$lme)
Then I think you should check if the fits were done via REML and also be
aware of the issue of testing wether a variance term is 0.
that did not seem to return anything useful for this question.
A related question is how to test the significance of adding a second
random effect to a model that already has a random effect, such as:
g3 <- gamm(y ~ xc +z+ s(int),family=binomial, weights=trial, random =
list(Case=~1, z=~1),correlation=corAR1())
g4 <- gamm(y ~ xc +z+ s(int),family=binomial, weights=trial, random =
list(Case=~1, z=~1, int=~1),correlation=corAR1())
Again, I think you need anova() on the $lme components.
HTH
G
Any help would be appreciated.
Thanks.
Will Shadish
********************************************
g1
$lme
Linear mixed-effects model fit by maximum likelihood
Data: data
Log-likelihood: -437.696
Fixed: fixed
X(Intercept) Xz Xint Xs(xc)Fx1
0.6738466 -2.5688317 0.0137415 -0.1801294
Random effects:
Formula: ~Xr - 1 | g
Structure: pdIdnot
Xr1 Xr2 Xr3 Xr4
Xr5 Xr6 Xr7 Xr8 Residual
StdDev: 0.0004377781 0.0004377781 0.0004377781 0.0004377781
0.0004377781
0.0004377781 0.0004377781 0.0004377781 1.693177
Correlation Structure: AR(1)
Formula: ~1 | g
Parameter estimate(s):
Phi
0.3110725
Variance function:
Structure: fixed weights
Formula: ~invwt
Number of Observations: 264
Number of Groups: 1
$gam
Family: binomial
Link function: logit
Formula:
y ~ s(xc) + z + int
Estimated degrees of freedom:
1 total = 4
attr(,"class")
[1] "gamm" "list"
****************************
> g2
$lme
Linear mixed-effects model fit by maximum likelihood
Data: data
Log-likelihood: -443.9495
Fixed: fixed
X(Intercept) Xz Xint Xs(xc)Fx1
0.720018143 -2.562155820 0.003457463 -0.045821030
Random effects:
Formula: ~Xr - 1 | g
Structure: pdIdnot
Xr1 Xr2 Xr3 Xr4
Xr5 Xr6 Xr7 Xr8
StdDev: 7.056078e-06 7.056078e-06 7.056078e-06 7.056078e-06
7.056078e-06
7.056078e-06 7.056078e-06 7.056078e-06
Formula: ~1 | xc %in% g
(Intercept) Residual
StdDev: 6.277279e-05 1.683007
Correlation Structure: AR(1)
Formula: ~1 | g/xc
Parameter estimate(s):
Phi
0.1809409
Variance function:
Structure: fixed weights
Formula: ~invwt
Number of Observations: 264
Number of Groups:
g xc %in% g
1 34
$gam
Family: binomial
Link function: logit
Formula:
y ~ s(xc) + z + int
Estimated degrees of freedom:
1 total = 4
attr(,"class")
[1] "gamm" "list"
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