# When parameters are dropped from fixed effects in lmer, drop corresponding random effects

If I fit an lmer() model with correlated fixed effects, by default it gives me a fit warning fixed-effect model matrix is rank deficient and returns the model with one or more parameters dropped.

For example:

set.seed(1030)
d = data.frame(y=rnorm(100), x1=c('a', 'b'), x2=c('c', 'd'), k=1:5)
lmer(y ~ x1 + x2 + (1 + x1 + x2 | k), d)


(plus convergence warnings etc)

This fits a model with one fixed-effect parameter dropped. Is it possible to also force it to drop the slopes that correspond to the dropped column(s)?

I found instructions on how to identify the bad columns manually, but my situation is this: I have an interaction of multilevel factors, where some combinations of factor levels never co-occur in the data. The factors are sum-coded, and I'd like to just fit the maximal model without hand-coding new columns for each contrast parameter, because I'm using lsmeans to calculate predicted marginal means. If I can keep the original factor coding then I can get also get an easily-interpretable output from lsmeans.

Edit: an example like my data

This is what I'm doing now:

set.seed(1030)

# level 3 of 'a' only occurs with level 3 of 'b'
x = expand.grid(a=1:3, b=1:3)
x = subset(x, !(a == 3 & b != 3))

d = data.frame(y=rnorm(700),
a=factor(x$a), b=factor(x$b),
k=factor(1:5))

library(lme4)
library(lsmeans)

# tmp for speed
lsm.options(disable.pbkrtest=TRUE)

# this model includes random slopes for factor level combinations that don't exist
m1 = lmer(y ~ a * b + (1 + a * b | k), data=d)

lsmeans(m1, ~ a | b)

# and then pairs() for comparisons


Is this (below) what you're suggesting, or is this not quite right?

# this model has a different random parameterization, but
# doesn't include slopes for non-existent combinations
m2 = lmer(y ~ a * b + (1 + droplevels(interaction(a, b)) | k), data=d)

lsmeans(m2, ~ a | b)
# produces the same results as above

• The results from lsmeans won't depend on how factors are coded. But some of the results may not be estimable -- NAs will be returned for those, again regardless of how they are coded. – Russ Lenth Oct 30 '15 at 21:59
• Right, lsmeans is giving me NAs exactly where I expect it to for the non-estimable cells & contrasts. I just mean that I want to be able to use lsmeans(model, ~ factor), where factor is a 3-level sum-coded factor that both lmer and lsmeans know how to deal with, rather than lsmeans(model, ~ factor_1 + factor_2), where factor_1 is a column coded as 1 for level 1, 0 for level 2, and -1 for level 3; and factor_2 is a column coded as 0 for level 1, 1 for level 2, and -1 for level 3. – user2034412 Oct 31 '15 at 1:00
• If I need to make those columns by hand so that I can exclude some combinations of them for the interaction slopes, then lsmeans won't know which combinations of values correspond to which factor levels, and I'll have to interpret that myself. – user2034412 Oct 31 '15 at 1:02
• Why not just create a new factor using interaction(factor1, factor2)? Or am I missing something? – Russ Lenth Oct 31 '15 at 2:03
• I'm not totally sure what you mean - I edited my question to include an example like my data. Thank you for your help, by the way! I really appreciate it. – user2034412 Oct 31 '15 at 18:17

## 1 Answer

I suggest something like this:

newd = transform(d, ab = interaction(a, b))
m2 = lmer(y ~ ab + (1 + ab | k), data = newd)
lsm = lsmeans(m2, ~ ab)
contrast(lsm, list(c1 = c(...), c2 = c(...), ...))


In other words, use the new factor ab, which consists of the combinations of a and b that actually occur in your dataset, as the one factor to use in the model in place of every usage of a and b. In the contrast call, put the coefficients for meaningful comparisons or contrasts among the levels of ab.