[R-lang] trouble with mixed-model

[T. Florian Jaeger]

Dear Francisco,

as Roger said, too strong correlations between the variances of the random
effects can lead to a singularity in the estimation of the
variance-covariance matrix for the random effects. This can also happen, if
any of the variances are indistinguishable from zero. Like Roger, I do not
have a clear understanding of the underlying fitting procedure, but too the
best of my knowledge the singularity is due to one of the underlying
parameters determining the random effects whose value is being optimized is
too close to zero.

I suggest the following: look at the a couple of different models. I would
start by comparing a model with only a random intercept vs. a model with
only the random slopes (the "type | spk" part). If a model with only the
random slopes does not converge, the singularity due to some of the levels
of "type" being indistinguishable with regard to their random effects and
you should do what Roger suggested. If the model with only random slopes
DOES converge, you can compare it against a model with only the random
intercept. Too a first approximation, you may use the model fit measures,
e.g. AIC to compare the two models. When you compare these models, keep in
mind that the slopes have more DFs than just the intercept. If a model with
only the random intercept has basically the same model fit quality as a
model with only the random slopes, than it seems that (given the fixed
effects that you are considering) the random slopes do not seem to do much (
i.e. the different types do not seem to affect your dependent variable, at
least not under the assumption that their effect is normally distributed).
Have a look at Baayen, Davidson, & Bates, 07 for more detail on how to
compare different models based on their random effects.

Florian

On 6/23/07, Francisco Torreira <ftorrei2 at uiuc.edu> 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.
>
> Thanks in advance,
> Francisco Torreira
>
> --
> Francisco Torreira
> PhD Candidate in Hispanic Linguistics
> University of Illinois at Urbana-Champaign
>
> https://netfiles.uiuc.edu/ftorrei2/www/index.html
> tel: (+1) 217 - 778 8510
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>
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