What is the difference between crossed random effects and multiple membership random effects?
Multiple membership is not the same as crossed random effects: In a crossed random effects model, each observation can be associated with a single level of multiple, independent random effects (i.e. the random effects do not have to be nested). In a multiple membership model, each observation can be associated with multiple levels of a single random effect.
lme4 supports fully crossed random effects (whereas
e.g. nlme does not), but not multiple membership models.
lmerMultiMember adds support for multiple membership models
to lme4, in addition to the existing support for fully
crossed random effects.
What are multiple membership models used for?
In general, multiple memberships models are useful when each observation in your data is not associated with just a single participant/patient/etc. but with multiple participants in variable compositions.
One example is team sports, where a team’s performance is attributable to the input of multiple players, but the players that a team starts in any given game may be variable. To derive a measure of an individual athlete’s performance, you’ll need to model the multiple membership structure.
Another example is in psychological experiments that involve multiple people interacting (e.g. iterated learning experiments). The outcome of an interaction depends on input from multiple participants, and unless there is a strict role assignment (e.g. one participant can talk, the other can only listen) it makes sense to model participant random effects using multiple membership.
lmerMultiMember is pretty new, but we’ve already heard
from researchers in various fields that they’re using it to extend
lme4 so they can model data that requires multiple
membership models. From marine ecology, where it has been used to model
species diversity off the California coast, to modeling health outcomes
in patients with multiple comorbidities, to modeling genomic data, to
the lead authors’ own work in experimental psychology.
If you’re using lmerMultiMember to model something new
and exciting, let us know!
lmerMultiMember assumes that levels of a random effect
are additive, but what if I don’t want to make that assumption?
It is true that lmerMultiMember assumes additive effects
(e.g. a relay race’s outcome is determined by the sum of individual
runner’s speeds) and that this assumption may not hold for whatever
process you are trying to model. Other assumptions than additivity can
be built into a multiple membership model, but at this point you are
probably going to need to write a custom Bayesian model in e.g. Stan. If
you think this is something you need to do, we recommend that you A)
really think hard about this assumption (additivity is pretty
reasonable, so make sure you really need to deviate from it) and B) send
us an email if you need any help.
lmerMultiMember says the number of levels in my
grouping factor exceeds the number of observations!
It is hard to fit random effects when there are not enough
observations for each level of the random effect.
lmerMultiMember requires you to have at least as many
observations as you have levels of each random effect, but this is the
absolute lower limit and you should absolutely strive to have more than
that for reliable estimation.
In lme4, the need to have at least as many observations
as levels of each random effect is a hard technical/mathematical
requirement. the math behind lmerMultiMember makes it
technically possible to fit models with fewer observations than levels
of a random effect in some cases, but determining the lowest acceptable
of number of observations for a given model is not trivial, so for now
we are simply using the same rule that lme4 uses for
convenience.
I tried using another package to plot/summarize/etc. an
lmerMultiMember model, but I got an error!
Since lmerMultiMember model objects behave much like
lme4 model objects (they “inherit” the model class from
lme4) you can generally use them as you would use an
lme4 model. However, some packages
(e.g. sjPlot) are very strict about recognizing models and
will sometimes reject lmerMultiMember models by throwing an
error.
Luckily, there is an easy workaround that is often successful, which
is to coerce the lmerMultiMember model object to have the
class of an lme4 or lmerTest model:
class(m_lmer) <- "lmerMod" # for lmer models
class(m_glmer) <- "glmerMod" # for glmer models
class(m_lmer) <- "lmerModLmerTest" # if you want to use lmerTest functionalityKeep in mind that this change is just a trick; it is a superficial
change and some packages may still throw errors. If this happens, please
help us help you by reporting the issue
on the lmerMultiMember Github repo, and we will take a look
to see if we can fix it/convince the author of the other package to add
support for lmerMultiMember.
Why are multiple membership models not part of lme4
already?
lme4 did not support multiple membership models
originally because it is a less common use-case than single membership
models and it turns out to be kind of hard to implement in an elegant
way. The combination of these issues probably makes it hard to justify
doing things like changing the lme4 syntax just to support
this functionality.
We’re not pushing to absorb lmerMultiMember into
lme4 either, because the latter is kind of in maintenance
mode and very stable, with most development focusing on compatibility
and bugfixes, while lmerMultiMember is still a little
experimental and might still undergo major changes.
How should I cite lmerMultiMember?
We appreciate you citing lmerMultiMember if you’re
publishing research that uses the package. You can find citation
information on the author
page.