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

[Ben Bolker]

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On 15-06-22 03:21 PM, Nicolas Deguines wrote:
> Thank you Thierry for the note and pointing out the the glmm wiki
> FAQ.
> 
> I understand the models are different but does anyone have more
> specifics regarding the meaning of coding a random effect on the
> slope of multiple fixed variables, ie what's the difference
> between: glmer(response ~ x1 + x2 + x3 + x4 +(x1|year) +(x2|year)
> +(x3|year) +(x4|year), … ) and glmer(response ~ x1 + x2 + x3 + x4
> +(x1 + x2 +x3 +x4 | year), … )
> 
> Best, Nicolas
> 
> 
> On Thu, Jun 11, 2015 at 10:17 AM, Thierry Onkelinx
> <thierry.onkelinx at inbo.be
>> wrote:
> 
>> Dear Nicolas,
>> 
>> Those models are different, hence you get different results. Note
>> that two levels are not enough to get stable variance estimates
>> for the random effect. See glmm wiki FAQ. Op 11-jun.-2015 18:39
>> schreef "Nicolas Deguines" <nicodeguines at gmail.com>:
>> 
>>> 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 like to start by emphasizing Thierry's point that it really
doesn't make sense to fit a random effect for a grouping variable with
only two levels.  That said, for future reference:


  Your first model fits slope *and* intercept for each response
separately; you probably want

 (1|year) + (0+x1|year) + (0+x2|year) + (0+x3|year)+(0+x4|year)

*or*

  (1+x1+x2+x3+x4||year)

instead.  Each of these fits 5 variance parameters, *assuming* the
random effects are uncorrelated.

  (x1+x2+x3+x4|year)  fits a 5x5 (including the intercept term)
variance-covariance matrix.  It is more general and arguably better
because it is robust to recentering -- the meaning and predictions of
the independent-terms model if you subtract a constant value from any
of the predictors -- but it is also much more complex and so may
overwhelm your data or your computer.  (This comes up in the current
Bates et al. "Parsimonious mixed models" vs Barr et al (2013) "Keep it
maximal" debate ...)




>>> 
>>> 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
>>> 
>>> _______________________________________________ 
>>> R-sig-mixed-models at r-project.org mailing list 
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>> 
>> 
> 
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> 
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