Dear All, I am trying to fit a 2-level random intercept logistic regression on a data set of 20,000 cases. The model is specified as the following:
Dear All, I am trying to fit a 2-level random intercept logistic regression on a data set of 20,000 cases. The model is specified as the following: m1 <- glmer(inftmort ~ as.factor(cohort) + (1|code), family=binomial, data=d) I got "Warning message: In mer_finalize(ans) : false convergence (8)" With the "verbose=TRUE" option, I was able to get the following iteration history: 0: 3456.4146: 1.15161 -3.99068 -0.498790 -0.122116 1: 3361.3370: 1.04044 -4.38172 -0.561756 -0.289991 2: 3303.7986: 1.48296 -4.40741 -0.566208 -0.259730 3: 3147.5537: 1.93037 -5.14388 -0.682530 -0.443006 4: 3123.6900: 2.10192 -5.18784 -0.685558 -0.428320 5: 2988.6287: 2.94890 -6.31023 -0.825286 -0.586282 6: 2958.3364: 3.25396 -6.88256 -0.316988 0.572428 7: 2853.7703: 4.22731 -7.44955 -0.279492 -0.294353 8: 2844.8476: 4.36583 -7.43902 -0.293111 -0.267308 9: 2843.2879: 4.39182 -7.44895 -0.298791 -0.265899 10: 2840.2676: 4.44288 -7.47103 -0.310477 -0.263945 11: 2839.0890: 4.46259 -7.48131 -0.315320 -0.263753 12: 2838.8550: 4.46649 -7.48344 -0.316292 -0.263745 13: 2838.3889: 4.47428 -7.48771 -0.318236 -0.263737 14: 2838.3703: 4.47459 -7.48788 -0.318314 -0.263738 15: 2838.2216: 4.47708 -7.48927 -0.318936 -0.263742 16: 2838.2157: 4.47718 -7.48932 -0.318961 -0.263742 17: 2838.2145: 4.47720 -7.48934 -0.318966 -0.263742 18: 2838.2121: 4.47724 -7.48936 -0.318976 -0.263742 19: 2838.2120: 4.47724 -7.48936 -0.318976 -0.263742 20: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 21: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 22: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 23: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 24: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 25: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 26: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 27: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 28: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 29: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 30: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 31: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 32: 2838.2118: 4.47724 -7.48936 -0.318977 -0.263742 33: 2837.8154: 4.46385 -7.47464 -0.495684 -0.263985 34: 2837.7613: 4.46641 -7.47053 -0.498335 -0.264014 35: 2837.6418: 4.47259 -7.46200 -0.501644 -0.264141 36: 2837.5982: 4.47485 -7.45928 -0.502598 -0.264214 37: 2837.5850: 4.47537 -7.45882 -0.502848 -0.264237 38: 2837.5307: 4.47674 -7.45848 -0.503216 -0.264313 39: 2837.5014: 4.47725 -7.45875 -0.503273 -0.264344 40: 2837.4955: 4.47735 -7.45881 -0.503284 -0.264350 41: 2837.4944: 4.47738 -7.45882 -0.503286 -0.264351 42: 2837.4941: 4.47738 -7.45882 -0.503287 -0.264351 43: 2837.4936: 4.47739 -7.45883 -0.503288 -0.264352 44: 2837.4935: 4.47739 -7.45883 -0.503288 -0.264352 45: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 46: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 47: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 48: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 49: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 50: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 51: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 52: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 53: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 54: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 55: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 56: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 57: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 58: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 59: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 60: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 61: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 62: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 63: 2837.4931: 4.47740 -7.45883 -0.503289 -0.264352 By the way, the same model can be fitted using Stata using xtlogit and xtmelogit; a simpler model without the random component can be estimated using R as: m <- glm(inftmort ~ as.factor(cohort), family=binomial, data=d) I was also able to get highly consistent results via MCMC simulation using MCMCglmm. It will be greatly appreciated if someone can give me some hints where to look further. Thanks. Best, Shige BTW, sorry about the earlier post, which was caused by a mistake.
On Tue, Feb 16, 2010 at 9:05 AM, Shige Song <shigesong at gmail.com> wrote:> Dear All,> I am trying to fit a 2-level random intercept logistic regression on a > data set of 20,000 cases. ?The model is specified as the following:> ?m1 <- glmer(inftmort ~ as.factor(cohort) + (1|code), family=binomial, data=d)> I got "Warning message: In mer_finalize(ans) : false convergence (8)"That message means that the optimizer function, nlminb, got stalled. It has converged but the point at which is has converged is not clearly the optimum. In many cases this just indicates that the optimizer is being overly cautious. However, it can also mean that the problem is ill-defined. The fact the the second parameter is -7.46 is likely the problem. A difference in the probability of infant mortality between levels of cohort on the order of -7.5 on the logit scale is huge. Do the estimated probabilities at this value of the parameters make sense? P.S. Questions of this sort may be more readily answered in the R-SIG-mixed-models mailing list.> With the "verbose=TRUE" option, I was able to get the following > iteration history: > > ?0: ? ? 3456.4146: ?1.15161 -3.99068 -0.498790 -0.122116 > ?1: ? ? 3361.3370: ?1.04044 -4.38172 -0.561756 -0.289991 > ?2: ? ? 3303.7986: ?1.48296 -4.40741 -0.566208 -0.259730 > ?3: ? ? 3147.5537: ?1.93037 -5.14388 -0.682530 -0.443006 > ?4: ? ? 3123.6900: ?2.10192 -5.18784 -0.685558 -0.428320 > ?5: ? ? 2988.6287: ?2.94890 -6.31023 -0.825286 -0.586282 > ?6: ? ? 2958.3364: ?3.25396 -6.88256 -0.316988 0.572428 > ?7: ? ? 2853.7703: ?4.22731 -7.44955 -0.279492 -0.294353 > ?8: ? ? 2844.8476: ?4.36583 -7.43902 -0.293111 -0.267308 > ?9: ? ? 2843.2879: ?4.39182 -7.44895 -0.298791 -0.265899 > ?10: ? ? 2840.2676: ?4.44288 -7.47103 -0.310477 -0.263945 > ?11: ? ? 2839.0890: ?4.46259 -7.48131 -0.315320 -0.263753 > ?12: ? ? 2838.8550: ?4.46649 -7.48344 -0.316292 -0.263745 > ?13: ? ? 2838.3889: ?4.47428 -7.48771 -0.318236 -0.263737 > ?14: ? ? 2838.3703: ?4.47459 -7.48788 -0.318314 -0.263738 > ?15: ? ? 2838.2216: ?4.47708 -7.48927 -0.318936 -0.263742 > ?16: ? ? 2838.2157: ?4.47718 -7.48932 -0.318961 -0.263742 > ?17: ? ? 2838.2145: ?4.47720 -7.48934 -0.318966 -0.263742 > ?18: ? ? 2838.2121: ?4.47724 -7.48936 -0.318976 -0.263742 > ?19: ? ? 2838.2120: ?4.47724 -7.48936 -0.318976 -0.263742 > ?20: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?21: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?22: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?23: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?24: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?25: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?26: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?27: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?28: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?29: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?30: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?31: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?32: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742 > ?33: ? ? 2837.8154: ?4.46385 -7.47464 -0.495684 -0.263985 > ?34: ? ? 2837.7613: ?4.46641 -7.47053 -0.498335 -0.264014 > ?35: ? ? 2837.6418: ?4.47259 -7.46200 -0.501644 -0.264141 > ?36: ? ? 2837.5982: ?4.47485 -7.45928 -0.502598 -0.264214 > ?37: ? ? 2837.5850: ?4.47537 -7.45882 -0.502848 -0.264237 > ?38: ? ? 2837.5307: ?4.47674 -7.45848 -0.503216 -0.264313 > ?39: ? ? 2837.5014: ?4.47725 -7.45875 -0.503273 -0.264344 > ?40: ? ? 2837.4955: ?4.47735 -7.45881 -0.503284 -0.264350 > ?41: ? ? 2837.4944: ?4.47738 -7.45882 -0.503286 -0.264351 > ?42: ? ? 2837.4941: ?4.47738 -7.45882 -0.503287 -0.264351 > ?43: ? ? 2837.4936: ?4.47739 -7.45883 -0.503288 -0.264352 > ?44: ? ? 2837.4935: ?4.47739 -7.45883 -0.503288 -0.264352 > ?45: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?46: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?47: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?48: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?49: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?50: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?51: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?52: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?53: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?54: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?55: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?56: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?57: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?58: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?59: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?60: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?61: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?62: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > ?63: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352 > > By the way, the same model can be fitted using Stata using xtlogit and > xtmelogit; a simpler model without the random component can be > estimated using R as: > > m <- glm(inftmort ~ as.factor(cohort), family=binomial, data=d) > > I was also able to get highly consistent results via MCMC simulation > using MCMCglmm. > > It will be greatly appreciated if someone can give me some hints where > to look further. Thanks. > > Best, > Shige > > BTW, sorry about the earlier post, which was caused by a mistake. > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >
Hi Doug,
Thanks. Next time I will post it to the R-SIG0-mixed-models mailing
list, as you suggested.
With respect to your question, the answer is no, these parameters do
not make sense. Here is the Stata output from "exactly" the same
model:
. xi:xtlogit inftmort i.cohort, i(code)
i.cohort _Icohort_1-3 (naturally coded; _Icohort_1 omitted)
Fitting comparison model:
Iteration 0: log likelihood = -1754.4476
Iteration 1: log likelihood = -1749.3366
Iteration 2: log likelihood = -1749.2491
Iteration 3: log likelihood = -1749.2491
Fitting full model:
tau = 0.0 log likelihood = -1749.2491
tau = 0.1 log likelihood = -1743.8418
tau = 0.2 log likelihood = -1739.0769
tau = 0.3 log likelihood = -1736.4914
tau = 0.4 log likelihood = -1739.5415
Iteration 0: log likelihood = -1736.4914
Iteration 1: log likelihood = -1722.6629
Iteration 2: log likelihood = -1694.9114
Iteration 3: log likelihood = -1694.6509
Iteration 4: log likelihood = -1694.649
Iteration 5: log likelihood = -1694.649
Random-effects logistic regression Number of obs = 21694
Group variable: code Number of groups = 10789
Random effects u_i ~ Gaussian Obs per group: min = 1
avg = 2.0
max = 9
Wald chi2(2) = 8.05
Log likelihood = -1694.649 Prob > chi2 =
0.0178
------------------------------------------------------------------------------
inftmort | Coef. Std. Err. z P>|z| [95% Conf.
Interval]
-------------+----------------------------------------------------------------
_Icohort_2 | -.5246846 .1850328 -2.84 0.005 -.8873422 -.1620269
_Icohort_3 | -.1424331 .140369 -1.01 0.310 -.4175513 .132685
_cons | -5.214642 .1839703 -28.35 0.000 -5.575217 -4.854067
-------------+----------------------------------------------------------------
/lnsig2u | .9232684 .1416214 .6456956 1.200841
-------------+----------------------------------------------------------------
sigma_u | 1.586665 .1123528 1.381055 1.822885
rho | .4335015 .0347791 .3669899 .5024984
------------------------------------------------------------------------------
Likelihood-ratio test of rho=0: chibar2(01) = 109.20 Prob >= chibar2 =
0.000
The difference is quite huge, and Stata did not have any difficulties
estimating this model, which makes feel that I might get some very
basic specification wrong in my R model...
Best,
Shige
On Tue, Feb 16, 2010 at 10:29 AM, Douglas Bates <bates at stat.wisc.edu>
wrote:> On Tue, Feb 16, 2010 at 9:05 AM, Shige Song <shigesong at gmail.com>
wrote:
>> Dear All,
>
>> I am trying to fit a 2-level random intercept logistic regression on a
>> data set of 20,000 cases. ?The model is specified as the following:
>
>> ?m1 <- glmer(inftmort ~ as.factor(cohort) + (1|code),
family=binomial, data=d)
>
>> I got "Warning message: In mer_finalize(ans) : false convergence
(8)"
>
> That message means that the optimizer function, nlminb, got stalled.
> It has converged but the point at which is has converged is not
> clearly the optimum. ?In many cases this just indicates that the
> optimizer is being overly cautious. ?However, it can also mean that
> the problem is ill-defined.
>
> The fact the the second parameter is -7.46 is likely the problem. ?A
> difference in the probability of infant mortality between levels of
> cohort on the order of -7.5 on the logit scale is huge. ? Do the
> estimated probabilities at this value of the parameters make sense?
>
> P.S. Questions of this sort may be more readily answered in the
> R-SIG-mixed-models mailing list.
>
>> With the "verbose=TRUE" option, I was able to get the
following
>> iteration history:
>>
>> ?0: ? ? 3456.4146: ?1.15161 -3.99068 -0.498790 -0.122116
>> ?1: ? ? 3361.3370: ?1.04044 -4.38172 -0.561756 -0.289991
>> ?2: ? ? 3303.7986: ?1.48296 -4.40741 -0.566208 -0.259730
>> ?3: ? ? 3147.5537: ?1.93037 -5.14388 -0.682530 -0.443006
>> ?4: ? ? 3123.6900: ?2.10192 -5.18784 -0.685558 -0.428320
>> ?5: ? ? 2988.6287: ?2.94890 -6.31023 -0.825286 -0.586282
>> ?6: ? ? 2958.3364: ?3.25396 -6.88256 -0.316988 0.572428
>> ?7: ? ? 2853.7703: ?4.22731 -7.44955 -0.279492 -0.294353
>> ?8: ? ? 2844.8476: ?4.36583 -7.43902 -0.293111 -0.267308
>> ?9: ? ? 2843.2879: ?4.39182 -7.44895 -0.298791 -0.265899
>> ?10: ? ? 2840.2676: ?4.44288 -7.47103 -0.310477 -0.263945
>> ?11: ? ? 2839.0890: ?4.46259 -7.48131 -0.315320 -0.263753
>> ?12: ? ? 2838.8550: ?4.46649 -7.48344 -0.316292 -0.263745
>> ?13: ? ? 2838.3889: ?4.47428 -7.48771 -0.318236 -0.263737
>> ?14: ? ? 2838.3703: ?4.47459 -7.48788 -0.318314 -0.263738
>> ?15: ? ? 2838.2216: ?4.47708 -7.48927 -0.318936 -0.263742
>> ?16: ? ? 2838.2157: ?4.47718 -7.48932 -0.318961 -0.263742
>> ?17: ? ? 2838.2145: ?4.47720 -7.48934 -0.318966 -0.263742
>> ?18: ? ? 2838.2121: ?4.47724 -7.48936 -0.318976 -0.263742
>> ?19: ? ? 2838.2120: ?4.47724 -7.48936 -0.318976 -0.263742
>> ?20: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?21: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?22: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?23: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?24: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?25: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?26: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?27: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?28: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?29: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?30: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?31: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?32: ? ? 2838.2118: ?4.47724 -7.48936 -0.318977 -0.263742
>> ?33: ? ? 2837.8154: ?4.46385 -7.47464 -0.495684 -0.263985
>> ?34: ? ? 2837.7613: ?4.46641 -7.47053 -0.498335 -0.264014
>> ?35: ? ? 2837.6418: ?4.47259 -7.46200 -0.501644 -0.264141
>> ?36: ? ? 2837.5982: ?4.47485 -7.45928 -0.502598 -0.264214
>> ?37: ? ? 2837.5850: ?4.47537 -7.45882 -0.502848 -0.264237
>> ?38: ? ? 2837.5307: ?4.47674 -7.45848 -0.503216 -0.264313
>> ?39: ? ? 2837.5014: ?4.47725 -7.45875 -0.503273 -0.264344
>> ?40: ? ? 2837.4955: ?4.47735 -7.45881 -0.503284 -0.264350
>> ?41: ? ? 2837.4944: ?4.47738 -7.45882 -0.503286 -0.264351
>> ?42: ? ? 2837.4941: ?4.47738 -7.45882 -0.503287 -0.264351
>> ?43: ? ? 2837.4936: ?4.47739 -7.45883 -0.503288 -0.264352
>> ?44: ? ? 2837.4935: ?4.47739 -7.45883 -0.503288 -0.264352
>> ?45: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?46: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?47: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?48: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?49: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?50: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?51: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?52: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?53: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?54: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?55: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?56: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?57: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?58: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?59: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?60: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?61: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?62: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>> ?63: ? ? 2837.4931: ?4.47740 -7.45883 -0.503289 -0.264352
>>
>> By the way, the same model can be fitted using Stata using xtlogit and
>> xtmelogit; a simpler model without the random component can be
>> estimated using R as:
>>
>> m <- glm(inftmort ~ as.factor(cohort), family=binomial, data=d)
>>
>> I was also able to get highly consistent results via MCMC simulation
>> using MCMCglmm.
>>
>> It will be greatly appreciated if someone can give me some hints where
>> to look further. Thanks.
>>
>> Best,
>> Shige
>>
>> BTW, sorry about the earlier post, which was caused by a mistake.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>