[R-sig-ME] contrasts and interactions with multi-level factors in glmer

[Ben Bolker]

Haldre Rogers <haldre1 at ...> writes:

> 
> Hello-


Just a quick follow-up so that the list isn't *completely* silent
on the topic.  I think the main reason you're not getting any answers
is (1) your question is complex (speaking just for myself, I look
at it and think "oh, that's kind of hairy -- maybe I'll have a chance
to look at that tomorrow ...") (2) I'm pretty sure that your questions
are more general linear-model-parameterization questions than specifically
(G)LMM questions, so people not be jumping in on the list.
 
> I conducted a field experiment where I added seedlings near and far from 
> conspecific trees at multiple plots at multiple sites on multiple 
> islands and recorded survival, among other things. Here, I'm trying to 
> determine the overall effect of distance (near vs far) on the proportion 
> of seeds that survived in each plot (site is a random effect). I'd also 
> like to determine whether the effect of distance varies by canopy 
> openness. Finally, I would like to test whether the effect of distance 
> differs between islands. I'm confused about how to set up the right 
> contrasts given the interactions, and how to interpret the output. 
> Treatment contrasts use a reference level, which is fine for distance 
> where 'near' is a meaningful reference level, but for 'island', the 
> reference level is not meaningful (i.e. it doesn't make sense to compare 
> each island to one arbitrarily chosen island). A link to my data, and 
> output from an example are below. This is for one species, but I have 
> data for six species total, and ideally, I'd like to compare these 
> effects between species (see question 2 below). I have three specific 
> questions at the bottom.

The quick answer is that you can use sum-to-zero contrasts
(contr.sum) for island, if you want, which will make the main effect
of distance be the (unweighted) average effect across islands.

> 
> Here's a link to the data: 
> https://www.dropbox.com/s/fregbu154zw7whz/aglaifen.csv
> 
>  > aglaiafen<-read.csv("aglaifen.csv")
>  > aglaiafen$dist<-factor(aglaiafen$dist, levels=c("near", "far"))
>  >
>  > #response is cbind(number of seedlings that survived/number of 
> seedlings that died), family = binomial
>  > #Three predictors- island, distance, and canopy openness
>  > #island has 4 levels (A, B, C, D). Island A is reference level by 
> default, but is not really meaningful as reference level.
>  > #dist has 2 levels, near and far, with near set as reference level.
>  > #centavgopen is centered at the mean canopy openness.
>  > #site is a random effect (3-5 sites per island, 4 islands). There are 
> usually 4 near plots and 4 far plots per site.
>  >
>  > #Here are three approaches to analysis that give qualitatively 
> similar answers, but I'm not sure which (if any) is the best approach.
>  >

  Sorry, I don't have time to dig through all of this ...
> 
> *Questions: *
>  > # 1) Is one of these methods (or some other method) best for testing 
> the effect of distance on survival relative to canopy openness and 
> island? Can I conclude that, for this species, there is not a distance 
> effect for island A, B or D, there isn't an interaction between distance 
> and openness, but that there was lower seedling survival in far plots on 
> island C? Is that lower relative only to near plots on islandC? Why 
> don't the coefficients for the interactions change when contrasts are 
> changed?
> 
>  > # 2) I have similar data for five other species, and I'd like to 
> compare the magnitude of the distance effect between species. Would 
> adding a species to the model (by adding species*island*distance and 
> species*openness*distance) be advisable, or is it better to just analyze 
> each species separately to avoid the challenges with interpreting 
> three-way interactions, especially in glmer's where options for 
> hypothesis testing are more limited than lm's or glm's? Again, I don't 
> really want to know the effect of one species relative to a reference 
> species, but simply compare the magnitude of the distance effect between 
> species- how do I set up my model to do that? I can share the full 
> dataset offline if that would help.

   Well, the three-way interaction *is* the magnitude of the
difference among species.  You could use drop1() to test the overall
effect of the interaction (i.e., the overall magnitude of among-island
differences in the island*distance and openness*distance effects)

>  > # 3) Is the use of confint(model, method="Wald") acceptable for 
> testing this? I tried using bootMer a few different ways (e.g. 
> bootMer(survm1, nsim=1000), using a couple different functions), but all 
> bootstrap runs fail each time I've tried. Likelihood ratio tests can 
> tell me whether a factor should be included in a model, but not 
> differences between levels of factors (e.g. islands or species). In 
> addition, results from LRT's are similar to those obtained using 
> confint. Setting up the glht (multcomp package) for this, given all of 
> the interactions and the continuous openness variable seems a bit 
> overwhelming.

   If confint() results are similar to *summary()* results then
confint(model,method="Wald") is OK ...  results from LRTs and
those using confint(model,method="profile") (i.e. the default)
*should* be identical ...