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Wrapper around lme4::lmer and lme4::glmer to add support for multiple membership random effects.


The package is not yet available on CRAN, but you can install it with the devtools package:



How to use lmerMultiMember

If you want to learn how to use lmerMultiMember, a good start would be finish reading this README. After that, you can check out the package vignettes for more information about specific topics:

  1. General introduction to multiple membership models
  2. Bradley-Terry models in lmerMultiMember
  3. The original multiple membership vignette (Ben Bolker’s worked example that inspired this package)
  4. Frequently Asked Questions

What is a multimembership random effect?

Let’s take authorship as an example: If we want to model some aspect of published journal articles, e.g. citations ~ word_count, we might want to account for variability caused by the authors of papers by using random intercepts. However, many papers don’t have just a single author. How do we account for author variability then?

One method could be to model each unique grouping of authors as a separate level of the random effect (i.e. “John A”, “Mary B”, “John A & Mary B”, and “Mary B & John A” are four different levels of the random effect) but this has the downside of not correctly attributing the variance to the individual authors in the groups.

Another option is to have separate random effects for each position in the author list (i.e. (1|author1) + (1|author2) + (1|author3) etc.) but while this does treat each author as a separate entity, it treats the same author as different people depending on where they occur in the author list, which is also a little strange.

The most natural option would be to associate each observation (journal article) with multiple levels (authors) of a single random effect. This is a multimembership random effect.

How to specify a multimembership random effect

Specifying a multimembership model in lmerMultiMember works just like specifying any other mixed effects model in lme4, with the addition of a membership matrix (or weight matrix). This sparse matrix contains rows for all the observations in your dataset and columns for each unique group member. For each observation, the matrix contains 1s for all the group members associated with it, with 0s everywhere else. (If group members should not have equal association strength, the 1s in the membership matrix can, in principle, be replaces with fractions to represent relative contributions, etc.) The model syntax could then be e.g. lmerMultiMember::lmer(citations ~ word_count + (1 | author), memberships = list(author = membership_matrix)).

Creating a membership matrix might seem a little daunting, but we provide a helper function lmerMultiMember::weights_from_vector that creates a membership matrix from a vector of group memberships in comma-separated strings (e.g. c("A,B", "A,B,C", "B", "C,A")) so if you have group memberships documented in your dataset it should be easy enough to create a membership matrix for you model.

Nested random effects groupings work a little differently

lmerMultiMember uses dummy variables and fake factors internally to ‘trick’ lme4 into accepting multiple membership random effects. Unfortunately, that system of dummies and fakes means that you can’t specify a nested multimembership random effects grouping using the normal formula syntax. For example, lmer(citations ~ word_count + (1 | journal/author), memberships = list(author = membership_matrix)) will throw an error, because the multiple membership author variable cannot be nested inside the journal grouping.

The solution for this issue is to pre-generate an indicator/weight matrix for the nested grouping using the provided lmerMultiMember::interaction_weights() function. For example, given a dataframe df with multimembership author and single membership journal grouping variables, in order to get nested groupings, we could do the following:

Wa <- weights_from_vectors(df$author)
Wj <- Matrix::fac2sparse(df$journal)  # convert single membership vars to an indicator matrix with fac2sparse()
Waj <- interaction_weights(Wa, Wj)
lmer(citations ~ word_count + (1 | journal) + (1 | authorXjournal), memberships = list(authorXjournal = Waj))


If you have any issues fitting models with lmerMultiMember, feel free to contact JP van Paridon at If you find an error or bug, please file an issue on the Github repository.