[R-sig-ME] lmer() vs. lme() gave different variance component estimates

[Jarrod Hadfield]

Both converge to the same answer on Fedora and Mac (Mac sessionInfo() below)

lmer(score~trt+(1|id/eye),dat, verbose=T, start=list(matrix(10),matrix(10)))
  0:     429.50725:  10.0000  10.0000
   1:     406.76151:  12.7962  11.2523
   2:     403.69482:  13.3016  12.8538
   3:     403.18712:  13.6918  13.5236
   4:     403.15738:  13.8230  13.6823
   5:     403.15696:  13.8432  13.6895
   6:     403.15694:  13.8467  13.6854
   7:     403.15694:  13.8475  13.6827
   8:     403.15694:  13.8474  13.6826

lmer(score~trt+(1|id/eye),dat, verbose=T, start=list(matrix(.81),matrix(.57)))

  1:     1304.7519:  2.42844  1.75398
   2:     776.66857:  6.30805  0.00000
   3:     657.56008:  7.73875  0.00000
   4:     514.89384:  10.7783 0.000123881
   5:     460.61372:  13.2310 0.00140974
   6:     434.88979:  15.6779 0.00908817
   7:     426.68762:  17.5388 0.0316599
   8:     424.89288:  18.6843 0.0743135
   9:     424.71437:  19.1269 0.132248
  10:     424.70495:  19.2146 0.203365
  11:     424.68492:  19.3175 0.420732
  12:     424.52038:  19.7021  1.39710
  13:     424.12511:  20.4042  3.37502
  14:     422.97192:  20.4400  4.91187
  15:     417.56194:  17.5366  5.92339
  16:     406.81181:  13.4830  17.5342
  17:     405.45194:  15.7947  12.4361
  18:     404.19817:  15.0352  12.5415
  19:     403.37771:  13.5806  13.0273
  20:     403.37260:  13.7001  14.5562
  21:     403.16170:  13.8571  13.8057
  22:     403.15707:  13.8372  13.6724
  23:     403.15694:  13.8483  13.6821
  24:     403.15694:  13.8473  13.6827
  25:     403.15694:  13.8474  13.6826

sessionInfo()
R version 2.10.1 (2009-12-14)
i386-apple-darwin9.8.0

locale:
[1] en_GB.UTF-8/en_GB.UTF-8/C/C/en_GB.UTF-8/en_GB.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base

other attached packages:
[1] lme4_0.999375-35   Matrix_0.999375-43 lattice_0.18-3

loaded via a namespace (and not attached):
[1] grid_2.10.1   nlme_3.1-96   stats4_2.10.1




Quoting Peter Dalgaard <pdalgd at gmail.com>:

> On 09/18/2010 11:24 AM, Jarrod Hadfield wrote:
>> Fedora Core 13 seems fine:
>>
>> Linear mixed model fit by REML
>> Formula: score ~ trt + (1 | id/eye)
>>     Data: dat
>>     AIC   BIC logLik deviance REMLdev
>>   425.2 474.2 -201.6    412.7   403.2
>> Random effects:
>>   Groups   Name        Variance Std.Dev.
>>   eye:id   (Intercept) 3.59532  1.89613
>>   id       (Intercept) 3.51024  1.87356
>>   Residual             0.01875  0.13693
>> Number of obs: 640, groups: eye:id, 160; id, 80
>
> Not in 32bit:
>
>> lmer(score~trt+(1|id/eye),dat)
> Linear mixed model fit by REML
> Formula: score ~ trt + (1 | id/eye)
>    Data: dat
>    AIC   BIC logLik deviance REMLdev
>  446.7 495.8 -212.4    430.9   424.7
> Random effects:
>  Groups   Name        Variance   Std.Dev.
>  eye:id   (Intercept) 6.9208e+00 2.6307e+00
>  id       (Intercept) 4.0996e-12 2.0248e-06
>  Residual             1.8750e-02 1.3693e-01
> Number of obs: 640, groups: eye:id, 160; id, 80
>
> Diddling the start values can change the result, though. Could you all try
>
> (a) setting verbose=T
> (b) try start=list(matrix(10),matrix(10))
> (c) same thing, but with .81 and .57
>
>
> In the (c) case, I get
>
>> l <- lmer(score~trt+(1|id/eye),dat,
> start=list(matrix(.81),matrix(.57)), verbose=T)
>   0:     2226.5319: 0.810000 0.570000
>   1:     1304.7507:  2.42844  1.75398
>   2:     776.66839:  6.30805  0.00000
>   3:     657.56008:  7.73875  0.00000
>   4:     514.89378:  10.7783  0.00000
>   5:     460.61371:  13.2310  0.00000
>   6:     434.88972:  15.6779 1.52026e-08
>   7:     426.68822:  17.5387 6.57868e-08
>   8:     424.89428:  18.6843 1.41900e-07
>   9:     424.71823:  19.1258 2.47916e-07
>  10:     424.71356:  19.2075 3.75766e-07
>  11:     424.71354:  19.2122 5.37851e-07
>  12:     424.71354:  19.2122 7.55161e-07
>
> which suggests an algorithm error where the parameters are getting stuck
> on the boundary. These values match the automatically generated starting
> values only to two digits, so I'm somewhat baffled that you apparently
> get something completely different in 64 bits!
>
> --
> Peter Dalgaard
> Center for Statistics, Copenhagen Business School
> Phone: (+45)38153501
> Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com
>
>



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