I agree with Ben. Theoretically, Laplace (lmer) provides a better
approximation.
Chunhao
Quoting Ben Bolker <[EMAIL PROTECTED]>:
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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