[R] gamm in mgcv random effect significance

[William Shadish]

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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