convergence problem with nlme() (PR#2369)

Full_Name: Jerome Asselin
Version: 1.6.1
OS: linux redhat 7.2
Submission from: (NULL) (142.103.173.179)



I am using the nlme package version 3.1-33.

I tried an example from the file "library/nlme/scripts/ch08.R" that comes
with the nlme package but I did not obtain convergence. I assume that
this example worked at some point in the past, but I cannot determine
why it is not working anymore. So I am unable to determine whether this
is a numerical bug or a documentation bug (in the file "ch08.R").

More specifically, I tried the example below (in which I added the
option msVerbose=T.)

library(nlme)
data(Quinidine)
control <- nlmeControl(msVerbose = T)
fm1Quin.nlme <-
  nlme(conc ~ quinModel(Subject, time, conc, dose, interval,
                        lV, lKa, lCl),
       data = Quinidine, fixed = lV + lKa + lCl ~ 1,
       random = pdDiag(lV + lCl ~ 1), groups =  ~ Subject,
       start = list(fixed = c(5, -0.3, 2)),
       na.action = NULL, naPattern =  ~ !is.na(conc), control = control)
#Error in nlme.formula(conc ~ quinModel(Subject, time, conc, dose, interval,  :
#        Maximum number of iterations reached without convergence

Below is the trace of the calculations by nlme().


iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.9645714 1.2393630
Function Value
[1] 1053.026
Gradient:
[1] -5.1732725 -0.3194242

iteration = 10
Parameter:
[1] 5.492493 1.275746
Function Value
[1] 1050.678
Gradient:
[1] -0.0004125939  0.0012034419

Iteration limit exceeded.  Algorithm failed.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 5.492303 0.860876
Function Value
[1] 1047.32
Gradient:
[1]  8.080429e-04 -8.308982e-06

iteration = 6
Parameter:
[1] -1772.4732661     0.3624312
Function Value
[1] 815.6329
Gradient:
[1]  9.726484e-25 -2.590048e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.7142093 0.8328863
Function Value
[1] 1045.966
Gradient:
[1] -2.701254  1.837528

iteration = 6
Parameter:
[1] 1.1387817 0.8237138
Function Value
[1] 1045.492
Gradient:
[1] -3.297258e-08  4.558449e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2190786 0.8233033
Function Value
[1] 1044.609
Gradient:
[1]  2.589381 -2.443006

iteration = 7
Parameter:
[1] 0.6880674 0.8342263
Function Value
[1] 1043.658
Gradient:
[1] -5.457107e-08 -1.710382e-06

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6867763 0.8348800
Function Value
[1] 1045.262
Gradient:
[1] -3.318076  2.320207

iteration = 7
Parameter:
[1] 1.2547275 0.8239144
Function Value
[1] 1044.541
Gradient:
[1]  1.496284e-08 -6.761539e-21

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2661227 0.8244986
Function Value
[1] 1044.441
Gradient:
[1]  2.642391 -2.502298

iteration = 1
Parameter:
[1] -1509.6490716     0.8231054
Function Value
[1] 826.5788
Gradient:
[1] 5.044484e-19 3.488575e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851074 0.8350764
Function Value
[1] 1045.189
Gradient:
[1] -3.359032  2.357977

iteration = 7
Parameter:
[1] 1.2648770 0.8239819
Function Value
[1] 1044.448
Gradient:
[1] -1.484278e-08 -4.556966e-08

Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2679928 0.8245302
Function Value
[1] 1044.427
Gradient:
[1]  2.646834 -2.508039

iteration = 1
Parameter:
[1] -1511.23183     0.82312
Function Value
[1] 826.1627
Gradient:
[1] 1.373859e-18 3.405617e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849866 0.8350863
Function Value
[1] 1045.184
Gradient:
[1] -3.361700  2.360219

iteration = 7
Parameter:
[1] 1.2654792 0.8239847
Function Value
[1] 1044.442
Gradient:
[1] -1.483571e-08 -2.278475e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.268088 0.824533
Function Value
[1] 1044.426
Gradient:
[1]  2.647101 -2.508261

iteration = 1
Parameter:
[1] -1511.3133956     0.8231232
Function Value
[1] 827.7616
Gradient:
[1] 1.046018e-18 3.410108e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6850998 0.8350804
Function Value
[1] 1045.188
Gradient:
[1] -3.359382  2.358456

iteration = 7
Parameter:
[1] 1.2650078 0.8239839
Function Value
[1] 1044.447
Gradient:
[1] -1.484124e-08  2.278477e-08

Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680136 0.8245307
Function Value
[1] 1044.426
Gradient:
[1]  2.646877 -2.508084

iteration = 1
Parameter:
[1] -1511.2495885     0.8231376
Function Value
[1] 827.6179
Gradient:
[1] 1.473509e-19 3.477226e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851144 0.8350799
Function Value
[1] 1045.188
Gradient:
[1] -3.359088  2.358286

iteration = 6
Parameter:
[1] 1.2649473 0.8239835
Function Value
[1] 1044.448
Gradient:
[1]  2.968390e-08 -6.835435e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.267994 0.824532
Function Value
[1] 1044.427
Gradient:
[1]  2.646853 -2.507863

iteration = 1
Parameter:
[1] -1511.2336349     0.8231352
Function Value
[1] 828.0258
Gradient:
[1] -6.701743e-20  3.365341e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851079 0.8350803
Function Value
[1] 1045.188
Gradient:
[1] -3.359215  2.358392

iteration = 7
Parameter:
[1] 1.2649721 0.8239836
Function Value
[1] 1044.447
Gradient:
[1] 1.484166e-08 4.556957e-08

Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.268001 0.824530
Function Value
[1] 1044.427
Gradient:
[1]  2.646867 -2.508106

iteration = 1
Parameter:
[1] -1511.2385145     0.8231441
Function Value
[1] 825.0983
Gradient:
[1] -9.146131e-19  3.823514e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849865 0.8350865
Function Value
[1] 1045.184
Gradient:
[1] -3.361722  2.360234

iteration = 6
Parameter:
[1] 1.265490 0.823985
Function Value
[1] 1044.442
Gradient:
[1] -1.254955e-20 -6.835423e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2681041 0.8245325
Function Value
[1] 1044.426
Gradient:
[1]  2.647101 -2.508336

iteration = 1
Parameter:
[1] -1511.3262872     0.8231335
Function Value
[1] 828.0964
Gradient:
[1] 2.680533e-19 3.401084e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6850990 0.8350805
Function Value
[1] 1045.188
Gradient:
[1] -3.359395  2.358484

iteration = 7
Parameter:
[1] 1.2650090 0.8239838
Function Value
[1] 1044.447
Gradient:
[1] -4.452368e-08 -2.278478e-08

Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680059 0.8245313
Function Value
[1] 1044.426
Gradient:
[1]  2.646886 -2.508011

iteration = 1
Parameter:
[1] -1511.24342     0.82312
Function Value
[1] 827.5457
Gradient:
[1] -1.234659e-18  3.430500e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851253 0.8350791
Function Value
[1] 1045.189
Gradient:
[1] -3.358850  2.358082

iteration = 7
Parameter:
[1] 1.2648953 0.8239834
Function Value
[1] 1044.448
Gradient:
[1] -1.800871e-20 -4.556957e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2679782 0.8245315
Function Value
[1] 1044.427
Gradient:
[1]  2.646833 -2.507868

iteration = 1
Parameter:
[1] -1511.2203466     0.8231246
Function Value
[1] 827.655
Gradient:
[1] -6.572921e-20  3.458212e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851108 0.8350802
Function Value
[1] 1045.188
Gradient:
[1] -3.359155  2.358352

iteration = 6
Parameter:
[1] 1.2649595 0.8239835
Function Value
[1] 1044.448
Gradient:
[1] 3.562034e-07 3.850629e-06

Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2679959 0.8245315
Function Value
[1] 1044.427
Gradient:
[1]  2.646857 -2.507940

iteration = 1
Parameter:
[1] -1511.2351449     0.8231327
Function Value
[1] 826.1662
Gradient:
[1] -1.488559e-18  3.469375e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849859 0.8350863
Function Value
[1] 1045.184
Gradient:
[1] -3.361721  2.360224

iteration = 7
Parameter:
[1] 1.2654851 0.8239848
Function Value
[1] 1044.442
Gradient:
[1] 1.483564e-08 2.278475e-08

Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680893 0.8245333
Function Value
[1] 1044.426
Gradient:
[1]  2.647108 -2.508211

iteration = 1
Parameter:
[1] -1511.3143179     0.8231573
Function Value
[1] 826.9291
Gradient:
[1] 2.104922e-20 3.529035e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849815 0.8350874
Function Value
[1] 1045.184
Gradient:
[1] -3.361846  2.360388

iteration = 6
Parameter:
[1] 1.265520 0.823985
Function Value
[1] 1044.442
Gradient:
[1] -2.967047e-08 -2.278474e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.268114 0.824533
Function Value
[1] 1044.426
Gradient:
[1]  2.647111 -2.508323

iteration = 1
Parameter:
[1] -1511.3346598     0.8231364
Function Value
[1] 827.9441
Gradient:
[1] 5.172025e-19 3.451115e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851007 0.8350806
Function Value
[1] 1045.188
Gradient:
[1] -3.359375  2.358493

iteration = 7
Parameter:
[1] 1.2650083 0.8239838
Function Value
[1] 1044.447
Gradient:
[1] -1.484124e-08 -2.278478e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680159 0.8245307
Function Value
[1] 1044.426
Gradient:
[1]  2.646879 -2.508084

iteration = 1
Parameter:
[1] -1511.2514358     0.8231329
Function Value
[1] 827.6347
Gradient:
[1] 1.392743e-18 3.408522e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851072 0.8350800
Function Value
[1] 1045.188
Gradient:
[1] -3.359213  2.358363

iteration = 6
Parameter:
[1] 1.2649669 0.8239834
Function Value
[1] 1044.447
Gradient:
[1] -1.484172e-08 -6.835436e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2679877 0.8245304
Function Value
[1] 1044.427
Gradient:
[1]  2.646868 -2.508028

iteration = 1
Parameter:
[1] -1511.2276862     0.8231314
Function Value
[1] 827.9284
Gradient:
[1] -8.458835e-19  3.418282e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851074 0.8350800
Function Value
[1] 1045.188
Gradient:
[1] -3.359220  2.358355

iteration = 7
Parameter:
[1] 1.2649721 0.8239837
Function Value
[1] 1044.447
Gradient:
[1]  2.968332e-08 -2.162905e-20

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680039 0.8245315
Function Value
[1] 1044.427
Gradient:
[1]  2.646863 -2.507970

iteration = 1
Parameter:
[1] -1511.2418099     0.8231307
Function Value
[1] 821.013
Gradient:
[1] -1.151748e-18  3.745284e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849946 0.8350861
Function Value
[1] 1045.184
Gradient:
[1] -3.361550  2.360118

iteration = 7
Parameter:
[1] 1.2654518 0.8239848
Function Value
[1] 1044.443
Gradient:
[1] -1.483603e-08  2.278475e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680745 0.8245337
Function Value
[1] 1044.426
Gradient:
[1]  2.647091 -2.508132

iteration = 1
Parameter:
[1] -1511.3021850     0.8231395
Function Value
[1] 826.9798
Gradient:
[1] -6.873270e-21  3.541503e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849805 0.8350871
Function Value
[1] 1045.184
Gradient:
[1] -3.361853  2.360357

iteration = 6
Parameter:
[1] 1.265518 0.823985
Function Value
[1] 1044.442
Gradient:
[1] -6.414965e-21 -2.748390e-21

Relative gradient close to zero.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680999 0.8245325
Function Value
[1] 1044.426
Gradient:
[1]  2.647123 -2.508339

iteration = 1
Parameter:
[1] -1511.3228120     0.8231412
Function Value
[1] 827.4251
Gradient:
[1] 2.387140e-18 3.362223e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6850398 0.8350784
Function Value
[1] 1045.187
Gradient:
[1] -3.360343  2.358820

iteration = 6
Parameter:
[1] 1.2651213 0.8239824
Function Value
[1] 1044.446
Gradient:
[1] -1.094700e-20  4.556963e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680295 0.8245309
Function Value
[1] 1044.426
Gradient:
[1]  2.646955 -2.508173

iteration = 1
Parameter:
[1] -1511.262920     0.823141
Function Value
[1] 825.304
Gradient:
[1] 1.503567e-20 3.453135e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849834 0.8350867
Function Value
[1] 1045.184
Gradient:
[1] -3.361774  2.360293

iteration = 6
Parameter:
[1] 1.2654961 0.8239848
Function Value
[1] 1044.442
Gradient:
[1]  1.483552e-08 -2.278475e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680917 0.8245322
Function Value
[1] 1044.426
Gradient:
[1]  2.647117 -2.508340

iteration = 1
Parameter:
[1] -1511.3158054     0.8231388
Function Value
[1] 824.6348
Gradient:
[1] 5.051808e-19 3.498065e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849795 0.8350869
Function Value
[1] 1045.184
Gradient:
[1] -3.361863  2.360350

iteration = 6
Parameter:
[1] 1.265517 0.823985
Function Value
[1] 1044.442
Gradient:
[1]  1.483527e-08 -2.819618e-20

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680970 0.8245325
Function Value
[1] 1044.426
Gradient:
[1]  2.647123 -2.508321

iteration = 1
Parameter:
[1] -1511.3203920     0.8231351
Function Value
[1] 827.997
Gradient:
[1] 2.985541e-19 3.389715e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6850997 0.8350809
Function Value
[1] 1045.188
Gradient:
[1] -3.359386  2.358541

iteration = 7
Parameter:
[1] 1.2650077 0.8239836
Function Value
[1] 1044.447
Gradient:
[1] -1.724167e-20 -4.556957e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2679931 0.8245322
Function Value
[1] 1044.426
Gradient:
[1]  2.646886 -2.507881

iteration = 1
Parameter:
[1] -1511.2332090     0.8231399
Function Value
[1] 827.8576
Gradient:
[1] -4.046823e-19  3.374292e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6851068 0.8350803
Function Value
[1] 1045.188
Gradient:
[1] -3.359240  2.358399

iteration = 7
Parameter:
[1] 1.2649779 0.8239836
Function Value
[1] 1044.447
Gradient:
[1]  1.484159e-08 -2.278478e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2680074 0.8245313
Function Value
[1] 1044.427
Gradient:
[1]  2.646866 -2.507996

iteration = 1
Parameter:
[1] -1511.2447019     0.8231283
Function Value
[1] 828.111
Gradient:
[1] 1.838670e-19 3.383300e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 0.6849700 0.8350883
Function Value
[1] 1045.183
Gradient:
[1] -3.362103  2.360611

iteration = 6
Parameter:
[1] 1.2655782 0.8239852
Function Value
[1] 1044.441
Gradient:
[1]  2.966911e-08 -4.556948e-08

Successive iterates within tolerance.
Current iterate is probably solution.

iteration = 0
Step:
[1] 0 0
Parameter:
[1] 1.2681166 0.8245338
Function Value
[1] 1044.426
Gradient:
[1]  2.647143 -2.508281

iteration = 1
Parameter:
[1] -1511.3374568     0.8231297
Function Value
[1] 827.5546
Gradient:
[1] -1.121176e-18  3.487243e+01

Maximum step size exceeded 5 consecutive times.
Either the function is unbounded below,
becomes asymptotic to a finite value
from above in some direction,
or stepmx is too small.

Error in nlme.formula(conc ~ quinModel(Subject, time, conc, dose, interval,  : 
	Maximum number of iterations reached without convergence
Execution halted