[R] GLM, LMER, GEE interpretation

[ctu at bigred.unl.edu]

I agree with Ben. Theoretically, Laplace (lmer) provides a better  
approximation.

Chunhao


Quoting Ben Bolker <bolker at ufl.edu>:

> Daniel Malter <daniel <at> umd.edu> writes:
>
>>
>> Hi, my dependent variable is a proportion ("prob.bind"), and the independent
>> variables are factors for group membership ("group") and a covariate
>> ("capacity"). I am interested in the effects of group, capacity, and their
>> interaction. Each subject is observed on all (4) levels of capacity (I use
>> capacity as a covariate because the effect of this variable is normatively
>> linear). I fit three models, but I am observing differences between the
>> three.
>>
>> The first model is a quasibinomial without any subject effects using glm.
>> The second is a random-effects model using lmer. The third model is a
>> generalized estimating equation using gee from the gee package in which I
>> cluster for the subject using an unstructured correlation matrix. The
>> results of the first and the third model almost coincide, but the second,
>> using lmer, shows an insginficant coefficient where I would expect a
>> significant one. The other 2 models show the coefficient significant. I do
>> not really have experience with gee. Therefore I apologize in advance for my
>> ignorant question whether one of lmer and gee is preferable over the other
>> in this setting?
>
> [glm]
> Coefficients:
>>                 Estimate Std. Error t value Pr(>|t|)
>> (Intercept)      -3.4274     0.4641  -7.386 1.10e-12 ***
>> capacity          0.9931     0.1281   7.754 9.55e-14 ***
>> group2            0.7242     0.6337   1.143  0.25392
>> group3            2.0264     0.6168   3.286  0.00112 **
>> capacity:group2  -0.1523     0.1764  -0.863  0.38864
>> capacity:group3  -0.3885     0.1742  -2.231  0.02633 *
>
> [lmer]
>> Generalized linear mixed model fit using Laplace
>> Formula: prob.bind ~ capacity * group + (1 | subject)
>>  Subset: c(combination == "gnl")
>>  Family: quasibinomial(logit link)
>  [snip]
>> Fixed effects:
>>                 Estimate Std. Error t value
>> (Intercept)      -3.8628     1.2701  -3.041
>> capacity          1.1219     0.1176   9.542
>> group2            0.9086     1.7905   0.507
>> group3            2.3700     1.7936   1.321
>> capacity:group2  -0.1745     0.1610  -1.083
>> capacity:group3  -0.3807     0.1622  -2.348
>
> [gee]
>> Coefficients:
>>                   Estimate Naive S.E.    Naive z Robust S.E.   Robust z
>> (Intercept)     -3.4798395  0.4910274 -7.0868545   0.4739913 -7.3415687
>> capacity         1.0149659  0.1366365  7.4282170   0.1284162  7.9037210
>> group2           0.7781014  0.6691731  1.1627806   0.7424769  1.0479807
>> group3           2.0720270  0.6527565  3.1742727   0.6234005  3.3237495
>> capacity:group2 -0.1750448  0.1877361 -0.9323982   0.2060484 -0.8495325
>> capacity:group3 -0.4021872  0.1865916 -2.1554413   0.1724780 -2.3318168
>>
>
>   I assume you're talking about the differences in
> the estimated standard errors of the group3 (and group2)
> parameters (everything else looks pretty similar)?
>
>   All else being equal I would trust lmer slightly more
> than gee (and the non-clustered glm is not reliable for
> inference in this situation, since it ignores the clustering) --
> but I'm pretty ignorant of gee, so take that with a grain of salt.
> I would make the following suggestions --
>
> 1. consider whether it even makes sense to test the
> significance of the group3 main effect in the presence
> of the capacity:group3 interaction.  Is the value capacity=0
> somehow intrinsically interesting?
>
> 2. all of these standard error estimates are pretty crude/
> rely on large-sample assumptions (how big is your data set?);
> unfortunately more sophisticated estimates of uncertainty
> are currently unavailable for GLMMs in lmer.  I would try
> your problem again with glmmML, just to check that it gives
> similar answers to lmer.
>
> 3. if you need more advice, consider asking this on r-sig-mixed
> instead ...
>
>   Ben Bolker
>
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