extracting p values for main effects of binomial glmm

An issue that has not been raised so far is whether the binomial or
 other GLM type variance takes account of all relevant observation
 level sources of variation.  This is pertinent for all
generalised linear mixed models.

Over-dispersed binomial or Poisson is in my experience much more 
common (certainly, e.g. in such areas as ecology) than binomial or
 Poisson.  The effect on the variance can be huge, multiplying by a
 factor of 3 or 4 or more.  More generally, the multiplier may not
be a constant factor.  This issue is most serious for comparisons
where the relevant variances are the observation level variances.

With glmer(), one way to handle this is to fit an observation level
 random effect; the multiplier is not then a constant factor.
glmer() did at one time allow a constant multiplier.  I think it
unfortunate that this was removed, as it restricted the options
available.

Using negative binomial errors is in principle another possibility,
but such models can be difficult to get to converge.  If the model
is wrong, it may well not converge, which is an obstacle to getting
to the point where one has something half-sensible that does
converge ? this is the case for glm.nb() as well as for
glmer.nb().

With predicted probabilities that are close to 0 or 1, or Poisson 
means that are close to 0, the Hauck-Donner effect where the
standard errors for Wald statistics become nonsense and
z-statistics become smaller as the distance between means that are
to be compared increases, is something more to worry about.

I guess the message is that this is treacherous territory, and it 
really is necessary to know what one is doing!

I?d like to echo Jonathon Baron?s comments on the ?main effects in
 the presence of interactions issue."

John Maindonald             email: john.maindonald at anu.edu.au 
Wellington, NZ

On 6/03/2015, at 0:25, Henrik Singmann 
<henrik.singmann at psychologie.uni-freiburg.de> wrote:

Hi,

As others have pointed out, the issue of obtaining p-values for 
effects is not trivial and there are pitfalls. Nevertheless I
think that the easiest way to obtain what you want is to use
mixed(..., method = "LRT") from package afex (full disclaimer: I
am the main author of said package and function).

mixed() takes care of some issues, such as using appropriate
coding and how to test main effects in the presence of
interactions, in not uncontroversial but sensible ways (e.g., it
does the latter by simply removing the main effect in a
brute-force manner from the model-matrix and compare the full
with the so reduced model). The way things are handled in mixed
might not be correct in all cases but may provide exactly the
combination of ease of use with sensible defaults that may be
helpful in your case. In other words, it tries to adopt an
approach often taken by commercial statistics packages.

You simply call mixed instead of glmer which fits and refits 
various versions of the model to provide likelihood-ratio tests
for all effects as you want them. Note however, that mixed()
cannot deal with the way you specify the model using cbind() as
dependent variable. What you need to do is compute the
proportions of "successes" and pass the number of observations as
weights. Assuming your data resides in a data.frame df this would
result in something along the following lines:


df$prop_weights <- df$Offspring + df$Eggs_Offspring 
df$proportion_hatched <- df$Offspring/df$prop_weights

m1 <- mixed(proportion_hatched ~ Diet * Infection_status * Day + 
(1|SubjectID) + (1|Day), data = df, family=binomial, weights = 
df$proportion_weights, method = "LRT")

However, as Ken Beath has said, the main effects may not be 
sensible given interactions. To asses the degree of this threat
for your data (which very much much depends on the type of
interaction and their size) I suggest to follow the excellent
advice of fortune(193) to "take the unusual step of plotting the
data." This can be done nicely with e.g., the effects package,
even for complicated interactions and binomial mixed models.

Hope this helps, Henrik


Am 04.03.2015 um 21:11 schrieb Megan Kutzer:

Hi,

I'm fairly new to mixed models and have done a lot of reading 
without much success. Unfortunately there is no one at my 
institution who is really familiar with them so I thought I
would try this list.

I'm running a binomial generalized linear mixed effects model
and I need p-values for the main effects. I know this isn't
entirely correct with this type of model but my supervisor
wants the p-values!

The model is:

glmer (Proportion hatched ~ Diet * Infection status * Day + 
(1|SubjectID) + (1|Day), family=binomial)

where,

Proportion hatched = cbind(Offspring, Eggs-Offspring) Diet is
a factor with 2 levels Infection status is a factor with 4
levels Day is a factor with 3 levels

Using Subject ID number and Day as random effects is supposed
to control for pseudoreplication in the model, although I am
not entirely sure that this is specified in the correct way. I
wanted to include experimental replicate here too but the model
failed to converge.

My question is: is there a way to get p-values for the main
fixed effects of Diet, Infection and Day?

If you need more specific model information or the model output
I would be happy to provide it.

Thanks, Megan

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-- Dr. Henrik Singmann Universit?t Z?rich, Schweiz 
http://singmann.org