lme4 convergence problem

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