[R-lang] trouble with mixed-model

[Roger Levy]

Francisco Torreira wrote:
> Hello,
> 
> I am fitting a mixed model that prompts the following warning messages:
> 
> Warning messages:
> 1: Estimated variance-covariance for factor 'spk' is singular
>  in: `LMEoptimize<-`(`*tmp*`, value = list(maxIter = 200L, tolerance =
> 1.49011611938477e-08,
> 2: nlminb returned message function evaluation limit reached without
> convergence (9)
>  in: `LMEoptimize<-`(`*tmp*`, value = list(maxIter = 200L, tolerance =
> 1.49011611938477e-08,
> 
> Although the model is fitted, R does not let me run simulations on it
> with mcmcamp(). This is the error message I get:
> 
>> mcmcsamp(full, n=10000)
> Error: inconsistent degrees of freedom and dimension
> Error in t(.Call(mer_MCMCsamp, object, saveb, n, trans, verbose, deviance)) :
> 	error in evaluating the argument 'x' in selecting a method for function 't
> 
> The model was:
> full <- lmer(an ~ type + (1 + type | spk) - 1)
> 
> My design included 5 speakers (spk) and 5 utterance types (type). For
> each combination of speaker and utterance type there were
> approximately 20 repetitions. If I fit a more reduced model with no
> random effect for type within speakers, as in lmer(an~type+(1|spk)),
> no warning appears. Here is the summary of my full model:
> 
> Linear mixed-effects model fit by REML
> Formula: an ~ 1 + type + (1 + type | spk) - 1
>   AIC  BIC logLik MLdeviance REMLdeviance
>  4663 4747  -2311       4653         4623
> Random effects:
>  Groups   Name        Variance Std.Dev. Corr
>  spk      (Intercept) 1568.3   39.601
>           typee       1037.3   32.208   -0.745
>           typeg       1303.7   36.107   -0.659  0.946
>           typei       1780.9   42.200   -0.778  0.976  0.864
>           typel        757.4   27.521   -0.725  0.839  0.826  0.865
>  Residual              598.8   24.470
> number of obs: 498, groups: spk, 5
> 
> Fixed effects:
>       Estimate Std. Error t value
> typea    78.87      17.88   4.410
> typee    18.49      12.13   1.524
> typeg    50.86      14.26   3.566
> typei    11.42      12.48   0.915
> typel    14.94      12.46   1.199
> 
> Correlation of Fixed Effects:
>       typea typee typeg typei
> typee 0.570
> typeg 0.491 0.898
> typei 0.240 0.851 0.722
> typel 0.699 0.758 0.739 0.622
> 
> I wonder if the high correlations correlations between several
> utterance types and the intercept in the random part of the model
> aren't causing all this trouble. I would appreciate any comment on the
> warnings.

Dear Francisco,

I think many of us have experienced problems with singular estimated 
variance-covariance matrices with lmer.  In some cases I am certain that 
the problem arises from near-perfect correlations between random 
effects, but I personally have not yet come to a deep understanding of 
what conditions can give rise to these near-perfect correlations.

A couple of possibilities: first, you can remove the 
intercept/utterance-type correlation term from your model by 
respecifying it as

  an ~ type + (1 | spk) + (0 + type | spk) - 1

and see whether this eliminates the singularity.  In your case, however, 
it seems like the strongest correlations are type pairs e&g and e&i. 
Perhaps you might try recoding utterance type (e.g., merge e & i since 
their coefficients seem similar anyway)?

Best & let us know if this helps,

Roger

-- 

Roger Levy                      Email: rlevy at ucsd.edu
Assistant Professor             Phone: 858-534-7219
Department of Linguistics       Fax:   858-534-4789
UC San Diego                    Web:   http://ling.ucsd.edu/~rlevy