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

[Tu Yu-Kang]

Dear Prof Bates,

> 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,  
> lm2<-lmer(ppd~month+(month|id),control = list(msVerbose = TRUE) ) 
  0      1191.73: 0.888889 0.0592593  0.00000
  1      1174.58: 5.00000e-10 5.00000e-10 0.281419
  2      1158.10: 0.956617 0.00924174 -0.00978256
  3      1151.88: 0.875101 5.00000e-10 0.550741
  4      1144.22: 0.605105 5.00000e-10 0.550741
  5      1142.59: 0.335108 5.00000e-10 0.550741
  6      1142.06: 0.452561 5.00000e-10 0.550741
  7      1141.97: 0.423318 5.00000e-10 0.550740
  8      1141.97: 0.416524 5.00000e-10 0.550740
  9      1141.97: 0.417039 5.00000e-10 0.550740
Warning message:
Estimated variance-covariance for factor 'id' is singular
 in: `LMEoptimize<-`(`*tmp*`, value = list(maxIter = 200, tolerance = 
1.49011611938477e-08,  
> lm3<-lmer2(ppd~month+(month|id),control = list(msVerbose = TRUE) ) 
  0      1191.73: 0.942809 0.243432  0.00000
  1      1181.40: 0.870948  0.00000 -0.124082
  2      1146.91: 0.855545 2.18615e-05 0.0163376
  3      1140.17: 0.413096  0.00000 0.0798584
  4      1137.48: 0.484553 2.13939e-09 0.179021
  5      1136.23: 0.542748  0.00000 0.0799814
  6      1135.87: 0.508893 0.0117775 0.110609
  7      1135.79: 0.496375  0.00000 0.115248
  8      1135.79: 0.497595  0.00000 0.117998
  9      1135.79: 0.494810 2.92361e-08 0.119135
 10      1135.79: 0.494925 1.82196e-08 0.119321
 11      1135.79: 0.495102  0.00000 0.119390
 12      1135.79: 0.495102  0.00000 0.119390
> 

The -2loglikelihhood from MLwiN is 1104.594. I did plot the data and they 
looked fine (at least to me).

With best regards,

Yu-Kang




>From: "Douglas Bates" <bates at stat.wisc.edu>
>To: "Tu Yu-Kang" <yukangtu at hotmail.com>
>CC: r-sig-mixed-models at r-project.org
>Subject: Re: [R] negative variances
>Date: Thu, 12 Apr 2007 08:07:57 -0500
>
>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