[R-sig-ME] Don't understand this variance components output

[Ben Bolker]

On 14-01-28 08:06 PM, Stuart Luppescu wrote:
> Hello, I'm analyzing ratings of teacher performance on 9 components.
> Each teacher is rated between 1 and 6 times. The average number of
> ratings per teacher is about 3.5. The structure of the data is (teachers
> nested within observations) crossed by components. The lmer call is:
>  
> lme6 <- lmer(rating ~ (1|tid.f) +  (1|comp.f) + (1|tid.f/obsorder.f),
> data=ratings, REML=FALSE)
> 
> The outcome is rating; tid.f is the teacher ID; comp.f is the component
> ID; obsorder.f is the observation. Here is the summary output:
> 
> Random effects:
>  Groups           Name        Variance Std.Dev.
>  obsorder.f.tid.f (Intercept) 0.06574  0.2564  
>  tid.f            (Intercept) 0.16309  0.4038  
>  tid.f.1          (Intercept) 0.03498  0.1870  
>  comp.f           (Intercept) 0.01589  0.1261  
>  Residual                     0.19696  0.4438  
> Number of obs: 166405, groups: obsorder.f:tid.f, 18496; tid.f, 5486;
> comp.f, 9
> 
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)  2.82680    0.04252   66.49
> 
> What I don't get is the line in the list of random effects labeled
> tid.f.1. What is this? Am I not specifying the model correctly?


tl;dr   just use (1|tid.f/obsorder.f), drop (1|tid.f) -- it's redundant.

  I don't know if it's a FAQ or not, but I feel like I've answered this
one before (maybe off-list though) ... the problem is that you've got
both (1|tid.f) (variation in intercepts among 'tid.f' levels) and
(1|tid.f/obsorder.f) (variation among obsorder.f nested within tid.f).
In particular, tid.f/obsorder.f expands to tid.f + tid.f:obsorder.f
(i.e., tid.f and obsorder.f nested within tid.f), so you have two tid.f
terms.  Unlike regular (e.g. lm/glm) formulae, these redundant terms
don't automatically get merged ...  I've tried to write code that would
reliably detect this sort of overparameterization, but so far I haven't
managed.

  Ben Bolker


> 
> Here is my sessionInfo:
> R version 3.0.2 (2013-09-25)
> Platform: x86_64-redhat-linux-gnu (64-bit)
> 
> locale:
>  [1] LC_CTYPE=en_US       LC_NUMERIC=C         LC_TIME=en_US       
>  [4] LC_COLLATE=en_US     LC_MONETARY=en_US    LC_MESSAGES=en_US   
>  [7] LC_PAPER=en_US       LC_NAME=C            LC_ADDRESS=C        
> [10] LC_TELEPHONE=C       LC_MEASUREMENT=en_US LC_IDENTIFICATION=C 
> 
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods
> base     
> 
> other attached packages:
>  [1] plyr_1.8        reshape2_1.2.2  MCMCglmm_2.17   corpcor_1.6.6  
>  [5] ape_3.0-11      coda_0.16-1     tensorA_0.36    MASS_7.3-29    
>  [9] foreign_0.8-59  lme4_1.0-5      Matrix_1.1-1.1  lattice_0.20-24
> 
> loaded via a namespace (and not attached):
> [1] compiler_3.0.2 grid_3.0.2     minqa_1.2.2    nlme_3.1-113
> splines_3.0.2 
> [6] stringr_0.6.2  tools_3.0.2   
> 
> Thanks very much for the help.
>