[R-sig-ME] [R] negative variances

[Douglas Bates]

On 4/12/07, Tu Yu-Kang <yukangtu at hotmail.com> wrote:
>
> Dear Prof Bates,
>
> Many thanks for your email. I tried lmer() and received the following
> messages:
>
> >  lm2<-lmer(ppd~month+(month|id))
> Warning message:
> Estimated variance-covariance for factor 'id' is singular
>  in: `LMEoptimize<-`(`*tmp*`, value = list(maxIter = 200, tolerance =
> 1.49011611938477e-08,
>
> I then tried lmer2():
>
> >  lm3<-lmer2(ppd~month+(month|id))
> > summary(lm3)
> Linear mixed-effects model fit by REML
>   AIC  BIC logLik MLdeviance REMLdeviance
>  1146 1166 -567.9       1126         1136
> Random effects:
>  Groups   Name        Variance  Std.Dev. Corr
>  id       (Intercept) 0.1566631 0.395807
>           month       0.0022331 0.047255 1.000
>  Residual             0.6391120 0.799445
> Number of obs: 420, groups: id, 140
>
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)  6.43595    0.07017   91.72
> month       -0.36619    0.01642  -22.30
>
> Correlation of Fixed Effects:
>       (Intr)
> month -0.544

I'm a bit pressed for time right now so this will be brief.  I suggest
that you add the optional argument

control = list(msVerbose = TRUE)

to the calls to lmer and to lmer2 and look at the progress of the
iterations and also at the value of the deviance.  I have seen
situations where lmer2 converges to a fit with a significantly smaller
deviance than can lmer because it progresses through the near-singular
region of the parameter space.

What was the deviance (or the log-likelihood) from the MLWin fit that
gave negative variance components?

Did you plot the data as ppd versus month by id using xyplot from the
lattice package?  That should always be the first step in the analysis
of longitudinal data.

> However, I am not sure about the results, because MLwiN showed both random
> effects were negative values (-0.196 and -0.023).
>
> I start to notice this problems of negative variances when I am learning
> how to use structural equation modeling software to run multilevel models
> for longitudinal data. To my great surprise, it occurs quite frequently. In
> SEM, this problem sometimes may be overcome by estimating  a nonlinear
> model by freeing the factor loadings. For example, in this data, PPD
> (probing pocket depth) was measured three times at month 0, 3 and 6. I only
> fixed the first and last factor loadings to be 0 and 6 to get a non-linear
> relation, and I also allow the level-1 residuals to be different on each
> occasion. However, in some data, I failed to get a satifactory model no
> matter how I modified my models.
>
> I looked for the discussion in several multilevel modeling textbooks but
> only found one short discussion in the book by Brown and Prescott. SEM
> literature usually suggest fixing the negative variances to 0. However, I
> wander whether this is the only way to get around this problem or the
> sensible way because if the random effects are fixed to 0 the model is no
> longer a random effects model.
>
> With best regards,
>
> Yu-Kang
>
> >From: "Douglas Bates" <bates at stat.wisc.edu>
> >To: "Tu Yu-Kang" <yukangtu at hotmail.com>
> >CC: r-help at stat.math.ethz.ch, r-sig-mixed-models at r-project.org
> >Subject: Re: [R] negative variances
> >Date: Wed, 11 Apr 2007 09:15:21 -0500
> >
> >On 4/11/07, Tu Yu-Kang <yukangtu at hotmail.com> wrote:
> >>Dear R experts,
> >>
> >>I had a question which may not be directly relevant to R but I will
> >>be
> >>grateful if you can give me some advices.
> >>
> >>I ran a two-level multilevel model for data with repeated
> >>measurements over
> >>time, i.e. level-1 the repeated measures and level-2 subjects. I
> >>could not
> >>get convergence using lme(), so I tried MLwiN, which eventually
> >>showed the
> >>level-2 variances (random effects for the intercept and slope) were
> >>negative values. I know this is known as Heywood cases in the
> >>structural
> >>equation modeling literature, but the only discussion on this
> >>problem in
> >>the literature of multilevel models and random effects models I can
> >>find is
> >>in the book by Prescott and Brown.
> >>
> >>Any suggestion on how to solve this problem will be highly
> >>appreciated.
> >
> >It is possible that the ML or REML estimates for a variance
> >component
> >can be zero.  The algorithm used in lme doesn't perform well in this
> >situation which is one reason that the lmer and lmer2 functions in
> >the
> >lme4 package were created.  Could you try fitting the model with
> >those
> >or provide us with the data so we can check it out?
> >
> >I recommend moving this discussion to the R-SIG-mixed-models mailing
> >list which I am copying on this reply.
>
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