lme4 convergence problem

Message: 3
Date: Fri, 14 Jan 2011 10:39:29 +1300
From: Murray Jorgensen<maj at stats.waikato.ac.nz>
To: R Mixed Models<r-sig-mixed-models at r-project.org>,  Doug and Martin
         <Matrix-authors at r-project.org>
Subject: [R-sig-ME] lme4 convergence problem
Message-ID:<4D2F7111.4070702 at stats.waikato.ac.nz>
Content-Type: text/plain; charset="iso-8859-1"; Format="flowed"

Dear List&  Maintainers,

I am currently running some scripts for some of the data sets in the
book by Andrew Gelman and Jennifer Hill. (2006). (Data Analysis Using
Regression and Multilevel/Hierarchical Models. Cambridge University
Press.) "arm"

However I have encountered a convergence difference between two versions
of R and its packages which seems to be a purely lme4 issue.

I have been mostly using a Dell laptop running Windows XP. Previously I
had been using R 2.11.1 but with packages at 2.10.1. Now I have brought
R and the packages both up to 2.12.1.

Here is my script: it uses the attached file which has itself been
constructed using a a script from the "arm" website but is self-contained.

library(lme4)
heights.clean =
read.table("C:\\Files\\R&Splus\\Gelman\\examples\\earnings\\heights.clean.txt",

                  header = TRUE)
attach(heights.clean)
y<- log(earn)
x<- height
n<- length(y)
n.age<- 3
n.eth<- 4
age<- age.category
# regression of log (earnings) on height, age, and ethnicity
M1<- lmer (y ~ x + (1 + x | eth))
summary (M1)
M1<- lmer (y ~ x + (1 + x | eth), verbose = TRUE)


Verbose output from R 2.12.1 and lme4_0.999375-37:

  >  M1<- lmer (y ~ x + (1 + x | eth), verbose = TRUE)

    0:     3113.7366: 0.0947958 0.00141417  0.00000
    1:     3113.5186:  0.00000  0.00000 -0.991536
    2:     3113.1254: 0.00106590 0.00111325 -0.991536
    3:     3112.9224: 0.000649400 0.000651990 -0.991536
    4:     3112.9133: 0.000831104 0.000668572 -0.990942
    5:     3112.9121: 0.000715470 0.000730468 -0.991549
    6:     3112.9117: 0.000904225 0.000536358 -0.990990
    7:     3112.9114: 0.000874136 0.000514266 -0.990990
    8:     3112.9112: 0.000889956 0.000518593 -0.990956
    9:     3112.9111: 0.000908394 0.000472281 -0.990901
   10:     3112.9110: 0.000923320 0.000460105 -0.990753
   11:     3112.9106: 0.000995159 0.000309059 -0.989729
   12:     3112.9103: 0.00103245  0.00000 -0.988338
   13:     3112.9103: 0.00104480 1.00631e-09 -0.988338
   14:     3112.9103: 0.00103952 1.72994e-08 -0.988327
   15:     3112.9103: 0.00103952 2.02562e-08 -0.988327
   16:     3112.9103: 0.00103951 2.01450e-08 -0.988327
   17:     3112.9103: 0.00103951 2.01450e-08 -0.988327
   18:     3112.9103: 0.00103951 2.01450e-08 -0.988327
Warning message:
In mer_finalize(ans) : false convergence (8)


Verbose output from R 2.11.1 and lme4_0.999375-32:

  >  M1<- lmer (y ~ x + (1 + x | eth), verbose = TRUE)

    0:     3113.7366: 0.0947958 0.00141417  0.00000
    1:     3113.5186:  0.00000  0.00000 -0.991536
    2:     3113.1254: 0.00106590 0.00111325 -0.991536
    3:     3112.9224: 0.000649400 0.000651990 -0.991536
    4:     3112.9133: 0.000831104 0.000668572 -0.990942
    5:     3112.9121: 0.000715470 0.000730468 -0.991549
    6:     3112.9117: 0.000904407 0.000536168 -0.990990
    7:     3112.9114: 0.000874337 0.000514111 -0.990990
    8:     3112.9112: 0.000890081 0.000518391 -0.990956
    9:     3112.9111: 0.000908420 0.000472254 -0.990901
   10:     3112.9110: 0.000923309 0.000460131 -0.990753
   11:     3112.9106: 0.000994079 0.000311231 -0.989738
   12:     3112.9103: 0.00103382  0.00000 -0.988215
   13:     3112.9102: 0.00103963 3.55942e-10 -0.988215
   14:     3112.9099: 0.00114005 0.000142779 -0.893828
   15:     3112.9099: 0.00113930 9.68963e-05 -0.893828
   16:     3112.9099: 0.00114352 9.70670e-05 -0.893805
   17:     3112.9099: 0.00114631 9.68698e-05 -0.893782
   18:     3112.9099: 0.00114593 8.96231e-05 -0.893737
   19:     3112.9099: 0.00114697 8.94093e-05 -0.893635
   20:     3112.9099: 0.00114840 8.74568e-05 -0.893534
   21:     3112.9099: 0.00114767 8.69236e-05 -0.893331
   22:     3112.9099: 0.00114960 8.45012e-05 -0.892925
   23:     3112.9097: 0.00119713 0.000103484 -0.854718
   24:     3112.9096: 0.00123584 0.000118803 -0.823861
   25:     3112.9094: 0.00128530 0.000135095 -0.793003
   26:     3112.9092: 0.00134505 0.000150925 -0.755646
   27:     3112.9088: 0.00148850 0.000172432 -0.680932
   28:     3112.9087: 0.00158189 0.000173348 -0.654113
   29:     3112.9080: 0.00172167 0.000172246 -0.591365
   30:     3112.9078: 0.00178884 0.000169040 -0.566266
   31:     3112.9071: 0.00202232 2.33096e-05 -0.506894
   32:     3112.9067: 0.00207199  0.00000 -0.501077
   33:     3112.9063: 0.00219029  0.00000 -0.475171
   34:     3112.9059: 0.00228481  0.00000 -0.456053
   35:     3112.9052: 0.00250518 6.54281e-05 -0.417817
   36:     3112.9048: 0.00260386 6.61956e-05 -0.402523
   37:     3112.9041: 0.00281388 6.37610e-05 -0.371934
   38:     3112.9037: 0.00294734 5.86692e-05 -0.358875
   39:     3112.9029: 0.00315988 1.53970e-05 -0.332756
   40:     3112.9023: 0.00333904 5.76185e-05 -0.315483
   41:     3112.9022: 0.00337566 5.68599e-05 -0.315484
   42:     3112.9022: 0.00337228 2.04001e-05 -0.315482
   43:     3112.9022: 0.00339045 1.50348e-05 -0.315412
   44:     3112.9022: 0.00338041 1.25433e-05 -0.315376
   45:     3112.9022: 0.00338454 4.34985e-07 -0.315304
   46:     3112.9007: 0.00380902 4.53446e-07 -0.277795
   47:     3112.9001: 0.00401754  0.00000 -0.262792
   48:     3112.8984: 0.00456608  0.00000 -0.231839
   49:     3112.8956: 0.00545144 1.95070e-06 -0.195416
   50:     3112.8928: 0.00652406 1.16379e-05 -0.175790
   51:     3112.8916: 0.00660908  0.00000 -0.163760
   52:     3112.8890: 0.00773482 4.99796e-06 -0.139726
   53:     3112.8806: 0.00972168  0.00000 -0.121025
   54:     3112.8786: 0.0114761 5.99051e-06 -0.0970285
   55:     3112.8760: 0.0109215 6.10952e-06 -0.107449
   56:     3112.8703: 0.0130487  0.00000 -0.0891341
   57:     3112.8672: 0.0146986  0.00000 -0.0791535
   58:     3112.8538: 0.0174766  0.00000 -0.0712682
   59:     3112.8464: 0.0196425 9.24134e-08 -0.0648869
   60:     3112.8229: 0.0261589 1.12351e-07 -0.0530892
   61:     3112.8218: 0.0301145  0.00000 -0.0522032
   62:     3112.8064: 0.0310301 2.94121e-08 -0.0482541
   63:     3112.7853: 0.0370813  0.00000 -0.0428581
   64:     3112.7768: 0.0392902 5.51626e-07 -0.0404835
   65:     3112.7574: 0.0448577  0.00000 -0.0371558
   66:     3112.7034: 0.0688045 9.08273e-06 -0.0271719
   67:     3112.5859: 0.0947196 0.000137210 -0.0259377
   68:     3112.5520: 0.120260  0.00000 -0.0214016
   69:     3112.4267: 0.138009  0.00000 -0.0220440
   70:     3112.2524: 0.241689  0.00000 -0.0175340
   71:     3112.0653: 0.252030 5.74985e-06 -0.0195906
   72:     3111.6754: 0.350688  0.00000 -0.0176928
   73:     3111.5729: 0.396312  0.00000 -0.0169346
   74:     3111.4491: 0.441941  0.00000 -0.0166439
   75:     3110.9290: 0.624460  0.00000 -0.0161161
   76:     3110.0355:  1.03912  0.00000 -0.0160134
   77:     3109.9542:  1.12017  0.00000 -0.0157653
   78:     3109.8078:  1.29685  0.00000 -0.0157324
   79:     3109.7519:  1.45344  0.00000 -0.0157254
   80:     3109.7469:  1.52828  0.00000 -0.0156867
   81:     3109.7461:  1.53677  0.00000 -0.0157060
   82:     3109.7460:  1.53350  0.00000 -0.0157010
   83:     3109.7460:  1.53352  0.00000 -0.0157010



The two iterations start off at the same values but start to diverge
around step 12.

Murray

--
Dr Murray Jorgensen      http://www.stats.waikato.ac.nz/Staff/maj.html
Department of Statistics, University of Waikato, Hamilton, New Zealand
Email: maj at waikato.ac.nz                                Fax 7 838 4155
Phone  +64 7 838 4773 wk    Home +64 7 825 0441   Mobile 021 0200 8350

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