# Re: [R] GLM, LMER, GEE interpretation

From: Daniel Malter <daniel_at_umd.edu>
Date: Mon, 07 Jul 2008 19:45:41 -0400

Thanks a lot.

Yes, I have looked at graphical summaries, but I would appreciate your opinion. I have uploaded three graphs that show the dependent variable versus capacity ( http://danielsresearch.blogspot.com/ ). The first shows it for the entire sample by group (groups are indicated by colors; values have been jittered so as to make it visible better). The second and third show the probability for each individual in a group. I selected another situation than the one I outlined before. But the problem is essentially the same. The difference is that in this example I only have two groups, not three.

Yes, I was fitting a quasibinomial gee. To check consistency, I let the gee compute the scale parameter and, alternatively, passed the scale parameter from the GLM (without random effects). Since the scale parameters are very similar, the results are basically identical between the two gees, which indicates that the "automatic" gee in fact uses the scale parameter it computes (and does not only display it to indicate that there is a problem).

I had also checked for a binomial lmer - which was the reason for checking a quasibinomial. If I am using a binomial lmer instead of a quasibinomial, I get (for the current two-group example):

```                       Estimate Std. Error z value Pr(>|z|)
(Intercept)            -1.43810    0.23280   -6.18 6.52e-10 ***
I(capacity - 2)         1.17367    0.02345   50.05  < 2e-16 ***
group2                  0.87093    0.32981    2.64  0.00827 **
```
I(capacity - 2):group2 -0.21686 0.03263 -6.65 3.00e-11 ***

AIC 6489, Estimated scale 4.78

whereas with the quasibinomial I get:

```                       Estimate Std. Error t value
(Intercept)             -1.4381     1.1117  -1.294
I(capacity - 2)          1.1737     0.1120  10.482
group2                   0.8709     1.5749   0.553
I(capacity - 2):group2  -0.2169     0.1558  -1.392

```

AIC 6468 The estimates are basically identical, but the standard errors are very different.

5. I indeed meant qualitatively similar results. Apologies for the sloppy wording. However, I also tried the reverse (i.e. 5-capacity), as you suggested, and find no significant group effects. This is not surprising as the groups tend to converge as capacity increases.

6. I thought that if I leave out the capacity variable and just model group+group:capacity I get the intercept for each group (whether they are different), and the capacity*group interaction would describe whether the "slope" of each group (if I may say so for binomial model) is different on average. So I would not describe a general capacity effect for which the group*capycity interactions would then describe a departure from the general capacity effect. Instead I would model the capacity "slope" directly for each group by just including the group*capacity interaction without the general capacity effect..

Daniel

cuncta stricte discussurus

-----Ursprüngliche Nachricht-----
Von: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] Im Auftrag von Ben Bolker
Gesendet: Monday, July 07, 2008 5:49 PM
An: r-help_at_stat.math.ethz.ch
Betreff: Re: [R] GLM, LMER, GEE interpretation

Daniel Malter <daniel <at> umd.edu> writes:

>
> However, it seems glmmML does not allow for a quasibinomial fit as I
> did with the models I used. I have large overdispersion which I
> account for using a quasibinomial with scaling parameter. Further, I
> have 360 observations - is that considered large enough for asymptotics?
>
> The capacity covariate ranges from 2 to 5 in steps of 1. I repeated
> the analysis subtracting 2 (because then the "0" capacity makes more
> sense and is of intrinsic interest) and get the "same" results. The
> group and group*capacity interaction make sense as I want to
> investigate a level and a slope difference for the groups. However, I
> am worried about the correlation of fixed effects. LMER gives me the
> following correlation matrix for the fixed effects:
>
> (Intr) I(c-2) group2 group3 I(-2):2
> I(capcty-2) -0.143
> group2 -0.707 0.101
> group3 -0.705 0.101 0.499
> I(c-2):grp2 0.104 -0.730 -0.135 -0.074
> I(c-2):grp3 0.104 -0.725 -0.073 -0.129 0.529
>
> I will try to leave out the capacity effect altogether and just model
> a group and a group slope effect. Does that make sense?
>
> Thanks,
> Daniel

Some quick (incomplete) answers (hoping for someone else to jump in):

1. overdispersion of 39 is very high, often indicates some nasty lack of fit -- have you looked at graphical summaries etc. to see that it's "just" high variance? Alternatively, this could just be telling you about the fact of clustering, and it's possible that your subject-specific random effect is taking care of the overdispersion. I don't know how to extract an estimate of the scale parameter from a (g)lmer fit though ... are you fitting quasibinomial, or binomial, in the GEE case? (One quick way to see if the scale parameter is big is to see if anything changes much if you run the (g)lmer model with binomial rather than QB.)
2. those correlations among parameters don't look *terribly* high to me -- I would worry about abs(c) > 0.8 ....
3. 360 observations (and 90 clusters) does seem pretty reasonable for 6 fixed parameters + 1 random effect ...
4. I wouldn't be 100% certain that glmer is handling QB right -- have you tried a simulation with known overdispersion parameters?
5. I'm surprised you can shift the origin on capacity and get the "same" results, although maybe you just mean significant one way/insignificant the other ... If it makes sense to compare groups at capacity=2, then testing the significance in this case seems OK, even in the presence of the group:capacity interaction. (Although consider what you would say if the answer changed if you modeled (capacity-5) rather than (capacity-2))
6. I don't understand what a "group slope effect" is ... ?

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