[R-sig-ME] lme4 - equal estimates of regression coefficients across levels of a random effect

[Nicolas Deguines]

Dear lme4 authors & users,

I’m a postdoctoral research scholar working on the effect of
precipitation on the food web of a grassland semi-arid ecosystem in
California.

I am analyzing my dataset with version 1.1-7 of the lme4 package with
version 3.2.0 of R.
I encountered an issue while running a glmer model that includes
random effects from a categorical variable (“year”, 2010 and 2011) on
the slope of four explanatory variables.
Precisely, the estimated slope coefficients for 1 out of 4 explanatory
variables are identical in the two years. However, when running a
model including only this particular explanatory variable and the same
random effect from year on slope, estimates are different for the two
years (indeed, I did check that values are different in the two years.

It also happens for other models I’m running, e.g. with that
particular explanatory variable + two new ones: this time though, the
slope coefficients are different for that particular variable but
identical for the two new ones (nb: the response variable in this
model differs from the 1st model discussed).

Is this an issue that already occurred to other lme4 users? Any idea
about what I may be doing wrong?
I suspect it may come from the syntax of my models. I had fitted my model as:
glmer(response ~ x1 + x2 + x3 + x4 +(x1|year) +(x2|year) +(x3|year)
+(x4|year), … )
But I tried the following model:
glmer(response ~ x1 + x2 + x3 + x4 +(x1 + x2 +x3 +x4 | year), … )
it does estimate different slope coefficients for each year.
I don’t know what meanings are associated with these two different
syntaxes though, and I would really appreciate any information or
reference anyone can give to clarify this.

I would be glad to provide additional information that may be needed
about the models or the dataset.

I take the opportunity while writing this email to thank lme4 authors
for developing and improving the very useful package that is lme4!

Best regards,
Nicolas Deguines