[R-sig-ME] lme4/nlmer problem
Douglas Bates
bates at stat.wisc.edu
Fri Aug 17 14:40:02 CEST 2007
A call to nlmer looks different from a call to nlme. The formula
argument should be a three-part formula of the form
response ~ nonlinear_model ~ mixed-model_formula
Some examples are shown below. I am "near" release of the development
version of the lme4 package that includes nlmer. I still need to
debug the version of glmer in this release. We will need to arrange
for a transition period so users can take previously fit lmer objects
and convert them to the new form. The source package for the
development version can be created from the sources in the SVN archive
https://svn.r-project.org/R-packages/branches/gappy-lmer/
I don't use Windows and do not have a Windows package for
installation. i can create one using Uwe's win-builder.R-project.org
if it is urgent. Otherwise I would suggest waiting until we transfer
the project to R-forge.R-project.org where the development version
will be build and tested every night.
On 8/17/07, Kalle Eerikäinen <kalle.eerikainen at metla.fi> wrote:
> Hi Markus,
>
> Many thanks for your message. Unfortunately, it makes no change whether
> or not the argument "fixed=p0+p1~1" is included into the model formula.
>
> Kalle
>
> Markus Jäntti wrote:
> > Kalle Eerikäinen wrote:
> >> Hello,
> >>
> >> I have done some test estimations using the lme4 package of R. The
> >> estimation of the parameters of linear mixed-effect models using the
> >> 'lmer' goes well. For instance, a very simple single-level mixed model
> >> "Naslund_lmer1 <- lmer(y ~ d13 + (1 |stand), data = height1)" for the
> >> relationship between the tree height (or its transformation) and
> >> diameter comes out perfectly.
> >>
> >> However, if I attempt to estimate nonlinear mixed-effect models, I
> >> always receive an error message that tells me: "Error:
> >> length(start$fixed) is not TRUE". This is also the case with the
> >> following model:
> >>
> >> Schumacher_nlmer1 <- lme4:::nlmer(ht ~ exp(p0 + p1*1/d13)+u0 ~
> >> (u0|stand) , fixed=p0+p1~1, data = height1, start = c(p0 = 0.1, p1 =
> >> -9.0), verb = 1)
> >
> > What is the purpose of the argument "fixed=p0+p1~1"? The help page makes
> > no mention of it. Maybe this is what is generating the error message.
> >
> > markus
> >>
> >
> >
> >> It is obvious that there exists a trivial bug/mistake in my code, but
> >> I cannot see what is wrong with it. Could someone give me a helping
> >> hand with my 'nlmer problem'?
> >>
> >> Regards,
> >>
> >> Kalle Eerikäinen
> example(lmer)
lmer> (fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy))
Linear mixed-effects model fit by REML
Formula: Reaction ~ Days + (Days | Subject)
Data: sleepstudy
AIC BIC logLik MLdeviance REMLdeviance
1754 1770 -871.8 1752 1744
Random effects:
Groups Name Variance Std.Dev. Corr
Subject 612.095 24.7405
35.071 5.9221 0.065
Residual 654.944 25.5919
Number of obs: 180, groups: Subject, 18
Fixed effects:
Estimate Std. Error t value
(Intercept) 251.405 6.825 36.84
Days 10.467 1.546 6.77
Correlation of Fixed Effects:
(Intr)
Days -0.138
lmer> (fm2 <- lmer(Reaction ~ Days + (1|Subject) + (0+Days|Subject),
sleepstudy))
Linear mixed-effects model fit by REML
Formula: Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
Data: sleepstudy
AIC BIC logLik MLdeviance REMLdeviance
1752 1764 -871.8 1752 1744
Random effects:
Groups Name Variance Std.Dev.
Subject 627.577 25.0515
Subject 35.852 5.9876
Residual 653.594 25.5655
Number of obs: 180, groups: Subject, 18; Subject, 18
Fixed effects:
Estimate Std. Error t value
(Intercept) 251.405 6.885 36.51
Days 10.467 1.559 6.71
Correlation of Fixed Effects:
(Intr)
Days -0.184
lmer> anova(fm1, fm2)
Data: sleepstudy
Models:
fm2: Reaction ~ Days + (1 | Subject) + (0 + Days | Subject)
fm1: Reaction ~ Days + (Days | Subject)
Df AIC BIC logLik Chisq Chi Df Pr(>Chisq)
fm2.p 4 1760.05 1772.82 -876.02
fm1.p 5 1761.99 1777.95 -875.99 0.0609 1 0.805
lmer> (nm1 <- nlmer(circumference ~ SSlogis(age, Asym, xmid, scal) ~ Asym|Tree,
lmer+ Orange, verb = 1, start = c(Asym = 200, xmid =
725, scal = 350)))
0: 299.40520: 0.617213 200.000 725.000 350.000
1: 273.38196: 1.61716 199.990 725.001 350.001
2: 268.17768: 2.12832 199.806 725.025 349.991
3: 265.29713: 2.68723 199.487 725.077 349.967
4: 264.04456: 3.19444 199.108 725.150 349.930
5: 263.54365: 3.63803 198.706 725.240 349.882
6: 263.39702: 3.95389 198.355 725.330 349.831
7: 263.36716: 4.12286 198.105 725.403 349.787
8: 263.35927: 4.19219 197.935 725.460 349.750
9: 263.34864: 4.25604 197.657 725.563 349.684
10: 263.32421: 4.34084 196.975 725.830 349.511
11: 263.27812: 4.41246 195.592 726.386 349.148
12: 263.21385: 4.39497 193.467 727.261 348.574
13: 263.16418: 4.24055 191.721 728.004 348.085
14: 263.14648: 4.07901 191.496 728.122 348.004
15: 263.14386: 4.03244 191.929 727.953 348.114
16: 263.14379: 4.03495 192.037 727.908 348.143
17: 263.14379: 4.03500 192.037 727.909 348.142
18: 263.14378: 4.03507 192.039 727.912 348.137
19: 263.14377: 4.03516 192.058 727.934 348.092
20: 263.14377: 4.03509 192.059 727.934 348.092
Nonlinear mixed model fit by Laplace
Formula: circumference ~ SSlogis(age, Asym, xmid, scal) ~ Asym | Tree
Data: Orange
Random effects:
Groups Name Variance Std.Dev.
Tree 1095.44 33.0975
Residual 67.28 8.2024
Number of obs: 35, groups: Tree, 5
Fixed effects:
Asym xmid scal
192.0589 727.9341 348.0919
lmer> (nm2 <- nlmer(conc ~ SSfol(Dose, Time,lKe, lKa, lCl) ~
(lKe+lKa+lCl|Subject),
lmer+ Theoph, start = c(lKe = -2.5, lKa = 0.5, lCl =
-3), verbose = 1))
0: 386.09968: 0.492366 0.492366 0.492366 0.00000 0.00000
0.00000 -2.50000 0.500000 -3.00000
1: 384.88844: 0.492038 0.492958 0.492286 -0.00561125 -0.00334076
-0.00230366 -2.49991 0.499929 -3.00040
2: 381.72748: 0.491706 0.493621 0.492187 -0.0103177 0.00147481
-0.00387406 -2.49971 0.499862 -3.00083
3: 378.94261: 0.491251 0.494615 0.492040 -0.0166021 -0.00115673
-0.00448798 -2.49934 0.499774 -3.00149
4: 377.39285: 0.490840 0.495891 0.491841 -0.0230831 0.000679450
-0.00400797 -2.49870 0.499687 -3.00236
5: 375.74378: 0.490427 0.498498 0.491398 -0.0284192 -0.000543731
-0.00618135 -2.49679 0.499589 -3.00411
6: 375.28979: 0.490375 0.499569 0.491218 -0.0301946 -0.000209774
-0.00465660 -2.49587 0.499576 -3.00483
7: 374.93047: 0.490232 0.500576 0.491053 -0.0318322 -0.000446596
-0.00650892 -2.49521 0.499528 -3.00552
8: 374.87512: 0.490216 0.500699 0.491032 -0.0320955 -3.46514e-05
-0.00643436 -2.49512 0.499524 -3.00561
9: 374.80736: 0.490203 0.500903 0.490997 -0.0323720 -0.000371694
-0.00640277 -2.49497 0.499519 -3.00575
10: 374.68230: 0.490180 0.501525 0.490889 -0.0327856 -5.04549e-05
-0.00657813 -2.49451 0.499506 -3.00618
11: 373.33408: 0.489949 0.513472 0.488761 -0.0368005 -0.000495062
-0.0110244 -2.48566 0.499303 -3.01444
12: 371.55810: 0.489649 0.526067 0.486246 -0.0398701 0.000796899
-0.00972192 -2.47684 0.499174 -3.02308
13: 370.08650: 0.489135 0.538835 0.483436 -0.0416520 -0.000892153
-0.00945036 -2.46818 0.499034 -3.03190
14: 368.56980: 0.488093 0.551720 0.479905 -0.0412694 0.000129599
-0.00929399 -2.46002 0.498898 -3.04099
15: 361.51477: 0.475950 0.684052 0.429743 -0.0257205 -0.00194058
-0.00365960 -2.39601 0.496206 -3.13671
16: 361.16262: 0.461171 0.807883 0.337864 -0.0637066 0.00266451
-0.00944405 -2.39669 0.488808 -3.22711
17: 354.97662: 0.430456 0.861847 0.284795 -0.0586136 -0.000373538
-0.0251852 -2.43362 0.492158 -3.23712
18: 352.94931: 0.391715 0.930566 0.270056 -0.0586716 0.00268354
-0.0188094 -2.47603 0.488436 -3.22586
19: 352.50958: 0.391680 0.930588 0.270078 -0.0590697 -0.00104861
-0.0177875 -2.47592 0.488454 -3.22589
20: 351.81346: 0.389032 0.929977 0.270567 -0.0593194 0.000716624
-0.0177630 -2.47413 0.489169 -3.22510
21: 351.77196: 0.386876 0.929332 0.270890 -0.0599408 0.000422051
-0.0172655 -2.47144 0.490263 -3.22421
22: 351.70183: 0.384614 0.928486 0.271183 -0.0602270 0.000947320
-0.0176223 -2.46906 0.491483 -3.22294
23: 351.64354: 0.381907 0.927674 0.271615 -0.0605585 0.000612578
-0.0177979 -2.46695 0.492636 -3.22198
24: 351.45295: 0.361792 0.920922 0.274368 -0.0626416 0.000948215
-0.0184277 -2.45587 0.500714 -3.22173
25: 351.41920: 0.340043 0.925736 0.263511 -0.0627954 0.000382087
-0.0181634 -2.45748 0.499773 -3.22745
26: 351.36176: 0.319527 0.936642 0.272866 -0.0634084 0.000640883
-0.0181702 -2.45989 0.496879 -3.22451
27: 351.35763: 0.319522 0.936663 0.272862 -0.0633127 0.000811601
-0.0181654 -2.45982 0.496886 -3.22453
28: 351.35398: 0.319514 0.936695 0.272856 -0.0631903 0.000687667
-0.0181293 -2.45972 0.496897 -3.22457
29: 351.34976: 0.319278 0.936827 0.272741 -0.0630328 0.000846531
-0.0181026 -2.45954 0.496867 -3.22447
30: 351.34465: 0.318678 0.937095 0.272459 -0.0629431 0.000681116
-0.0180636 -2.45934 0.496770 -3.22413
31: 351.33832: 0.317346 0.937578 0.271910 -0.0627742 0.000842182
-0.0180250 -2.45900 0.496565 -3.22354
32: 351.32914: 0.314176 0.938064 0.271044 -0.0625923 0.000668059
-0.0179401 -2.45882 0.496133 -3.22318
33: 351.29439: 0.285503 0.934514 0.269028 -0.0604029 0.000717185
-0.0171005 -2.46262 0.493595 -3.23365
34: 351.22704: 0.255183 0.937197 0.263394 -0.0572005 9.67627e-05
-0.0158327 -2.46159 0.491972 -3.23286
35: 351.17757: 0.224719 0.940024 0.257824 -0.0554810 0.000966560
-0.0153756 -2.46183 0.490199 -3.23206
36: 351.15197: 0.194079 0.944209 0.255029 -0.0535618 0.000374553
-0.0146192 -2.46285 0.492320 -3.23134
37: 351.11990: 0.220162 0.951637 0.269429 -0.0533941 0.000422727
-0.0150733 -2.46169 0.497667 -3.22999
38: 351.07908: 0.237936 0.970464 0.270589 -0.0549069 0.000977890
-0.0156717 -2.45577 0.481794 -3.22638
39: 351.04280: 0.252398 0.986541 0.268059 -0.0566637 0.000413897
-0.0162241 -2.45778 0.503965 -3.22759
40: 351.03651: 0.250609 0.985292 0.268665 -0.0555838 0.000793777
-0.0154951 -2.45641 0.509033 -3.22700
41: 351.02001: 0.249118 0.983275 0.269207 -0.0547708 0.000399987
-0.0155318 -2.45505 0.504024 -3.22628
42: 351.01884: 0.246330 0.987848 0.268166 -0.0540239 0.000759755
-0.0159234 -2.45462 0.502039 -3.22590
43: 351.00355: 0.245350 0.987979 0.268552 -0.0539114 0.000430733
-0.0155863 -2.45398 0.499423 -3.22558
44: 351.00194: 0.243729 0.989303 0.269419 -0.0536648 0.000630739
-0.0151864 -2.45254 0.494226 -3.22494
45: 350.99261: 0.243157 0.994940 0.269152 -0.0540473 0.000474664
-0.0153853 -2.45275 0.495783 -3.22509
46: 350.97638: 0.251550 1.01754 0.268227 -0.0538946 0.000480603
-0.0154727 -2.45108 0.504181 -3.22516
47: 350.97018: 0.248046 1.02234 0.269093 -0.0529578 0.000372733
-0.0154663 -2.44907 0.496315 -3.22439
48: 350.96949: 0.244190 1.02531 0.269006 -0.0531794 0.000428105
-0.0154698 -2.44957 0.496147 -3.22475
49: 350.96929: 0.248611 1.02686 0.270018 -0.0535457 0.000415639
-0.0155669 -2.44946 0.495945 -3.22572
50: 350.96917: 0.246859 1.02631 0.269920 -0.0532843 0.000400073
-0.0154960 -2.44968 0.496594 -3.22596
51: 350.96912: 0.245792 1.02604 0.269656 -0.0532195 0.000403823
-0.0154806 -2.44961 0.496563 -3.22551
52: 350.96912: 0.245999 1.02613 0.269687 -0.0532265 0.000403255
-0.0154822 -2.44965 0.496527 -3.22560
53: 350.96912: 0.246003 1.02610 0.269697 -0.0532315 0.000403090
-0.0154834 -2.44963 0.496558 -3.22560
54: 350.96912: 0.245997 1.02611 0.269692 -0.0532292 0.000403164
-0.0154828 -2.44964 0.496546 -3.22560
55: 350.96912: 0.245997 1.02611 0.269692 -0.0532292 0.000403165
-0.0154828 -2.44964 0.496546 -3.22560
Nonlinear mixed model fit by Laplace
Formula: conc ~ SSfol(Dose, Time, lKe, lKa, lCl) ~ (lKe + lKa + lCl |
Subject)
Data: Theoph
Random effects:
Groups Name Variance Std.Dev. Corr
Subject 0.029956 0.17308
0.521301 0.72201 -0.013
0.036130 0.19008 0.000 -0.059
Residual 0.495029 0.70358
Number of obs: 132, groups: Subject, 12
Fixed effects:
lKe lKa lCl
-2.4496370 0.4965462 -3.2256163
lmer> (nm3 <- nlmer(conc ~ SSfol(Dose, Time,lKe, lKa, lCl) ~
lmer+ (lKe|Subject) + (lKa|Subject) + (lCl|Subject), Theoph,
lmer+ start = c(lKe = -2.5, lKa = 0.5, lCl = -3), verbose = 1))
0: 386.09968: 0.492366 0.492366 0.492366 -2.50000 0.500000 -3.00000
1: 377.43545: 0.0825471 1.23161 0.393063 -2.38231 0.411355 -3.50398
2: 366.00277: 0.112039 1.21790 0.461466 -2.57362 0.412740 -3.33669
3: 360.02522: 0.162062 1.15605 0.375272 -2.39847 0.435753 -3.17745
4: 357.53543: 0.133920 1.14625 0.328917 -2.46420 0.437507 -3.19196
5: 355.97764: 0.0867116 1.13276 0.279073 -2.43653 0.442893 -3.23534
6: 355.27369: 0.0718404 1.12642 0.264747 -2.46936 0.444271 -3.21897
7: 354.97499: 0.0464245 1.11570 0.247811 -2.44891 0.448129 -3.23724
8: 354.69747: 0.0300521 1.10541 0.245427 -2.47167 0.450630 -3.22029
9: 354.44380: 0.0113476 1.08241 0.247659 -2.45877 0.456802 -3.23041
10: 354.30407: 0.0106401 1.05289 0.234811 -2.46665 0.463454 -3.22351
11: 354.17495: 0.0111025 1.02220 0.243825 -2.46532 0.469804 -3.23472
12: 354.07980: 0.00619672 0.990430 0.238104 -2.46637 0.474160 -3.22448
13: 354.06447: 0.00476224 0.987768 0.238322 -2.46122 0.474818 -3.23062
14: 354.04416: 0.00549549 0.981257 0.239218 -2.46669 0.475108 -3.23036
15: 354.03247: 0.00462216 0.974265 0.236284 -2.46289 0.476168 -3.23060
16: 354.00978: 0.00332796 0.958014 0.239023 -2.46434 0.476629 -3.22613
17: 354.00268: 0.00263076 0.953403 0.238980 -2.46373 0.477606 -3.23179
18: 353.99869: 0.00561923 0.948876 0.236087 -2.46739 0.479069 -3.23041
19: 353.99299: 0.00000 0.947792 0.238852 -2.46573 0.480566 -3.23083
20: 353.99084: 0.00000 0.946198 0.236413 -2.46555 0.480836 -3.23022
21: 353.98958: 2.84393e-11 0.943787 0.237974 -2.46491 0.481186 -3.23065
22: 353.98840: 0.000535840 0.941514 0.237039 -2.46633 0.481093 -3.22986
23: 353.98700: 0.00173219 0.939219 0.236789 -2.46529 0.480775 -3.23087
24: 353.98595: 0.00110715 0.936591 0.237723 -2.46594 0.480285 -3.23052
25: 353.98506: 0.00112750 0.935243 0.236653 -2.46543 0.482676 -3.23039
26: 353.98465: 0.00000 0.933278 0.237169 -2.46590 0.481052 -3.23009
27: 353.98452: 0.00000 0.931806 0.236825 -2.46509 0.479685 -3.23084
28: 353.98407: 0.000981068 0.930591 0.236833 -2.46573 0.481267 -3.23069
29: 353.98390: 0.000380416 0.930199 0.236642 -2.46544 0.481447 -3.23018
30: 353.98386: 0.000194769 0.929921 0.236808 -2.46537 0.481545 -3.23043
31: 353.98381: 8.11621e-05 0.929672 0.236742 -2.46558 0.481823 -3.23030
32: 353.98378: 0.000138324 0.929240 0.236665 -2.46546 0.481748 -3.23036
33: 353.98375: 0.000130336 0.928850 0.236742 -2.46551 0.481972 -3.23027
34: 353.98373: 0.00000 0.928494 0.236666 -2.46553 0.481790 -3.23040
35: 353.98372: 1.53639e-05 0.928261 0.236665 -2.46551 0.482194 -3.23037
36: 353.98372: 1.18744e-05 0.928223 0.236687 -2.46554 0.482191 -3.23034
37: 353.98372: 8.34650e-06 0.928177 0.236693 -2.46551 0.482190 -3.23036
38: 353.98371: 2.79048e-05 0.928069 0.236682 -2.46553 0.482143 -3.23033
39: 353.98371: 6.40584e-05 0.927846 0.236665 -2.46549 0.482045 -3.23034
40: 353.98371: 0.00000 0.927624 0.236703 -2.46553 0.482091 -3.23035
41: 353.98371: 0.00000 0.927553 0.236661 -2.46554 0.482132 -3.23036
42: 353.98371: 5.96124e-06 0.927462 0.236670 -2.46552 0.482124 -3.23035
43: 353.98371: 5.96124e-06 0.927462 0.236670 -2.46552 0.482124 -3.23035
Nonlinear mixed model fit by Laplace
Formula: conc ~ SSfol(Dose, Time, lKe, lKa, lCl) ~ (lKe | Subject) +
(lKa | Subject) + (lCl | Subject)
Data: Theoph
Random effects:
Groups Name Variance Std.Dev.
Subject 0.000000 0.00000
Subject 0.440903 0.66401
Subject 0.028714 0.16945
Residual 0.512588 0.71595
Number of obs: 132, groups: Subject, 12; Subject, 12; Subject, 12
Fixed effects:
lKe lKa lCl
-2.4655320 0.4821415 -3.2303559
lmer> (nm4 <- nlmer(conc ~ SSfol(Dose, Time,lKe, lKa, lCl) ~ (lKa+lCl|Subject),
lmer+ Theoph, start = c(lKe = -2.5, lKa = 0.5, lCl =
-3), verbose = 1))
0: 377.00821: 0.492366 0.492366 0.00000 -2.50000 0.500000 -3.00000
1: 375.06636: 0.496628 0.491116 0.115284 -2.49669 0.499833 -3.00310
2: 368.73772: 0.418871 0.467676 0.109343 -2.35636 0.496774 -3.12849
3: 360.04981: 0.402170 0.453340 0.0643095 -2.39295 0.495044 -3.13138
4: 358.31247: 0.398371 0.448441 0.0509030 -2.40073 0.494430 -3.13321
5: 357.53116: 0.391620 0.435052 0.0276480 -2.41896 0.492729 -3.13855
6: 355.71678: 0.387375 0.415764 0.0480068 -2.42360 0.490169 -3.15578
7: 351.92166: 0.324845 0.256277 0.0457815 -2.43077 0.474642 -3.28062
8: 350.29390: 0.325207 0.256363 0.0582163 -2.45170 0.473363 -3.26257
9: 349.96730: 0.317341 0.252784 0.0418845 -2.46832 0.472434 -3.24521
10: 349.38606: 0.308708 0.235571 0.0592500 -2.46265 0.472845 -3.23054
11: 349.18344: 0.278968 0.238355 0.0619188 -2.46058 0.473807 -3.22663
12: 349.13588: 0.256679 0.253837 0.0727460 -2.46387 0.474327 -3.23405
13: 348.96171: 0.233013 0.237400 0.0771499 -2.46412 0.474256 -3.22567
14: 348.75767: 0.185282 0.237304 0.112341 -2.45487 0.480483 -3.21946
15: 348.75117: 0.175838 0.237215 0.108856 -2.45946 0.477093 -3.22310
16: 348.69939: 0.176307 0.237053 0.116914 -2.45842 0.468137 -3.22395
17: 348.67673: 0.167417 0.237420 0.120847 -2.45913 0.475105 -3.22583
18: 348.66522: 0.151724 0.238434 0.137320 -2.45369 0.474436 -3.21949
19: 348.64376: 0.153956 0.236286 0.141555 -2.45956 0.473758 -3.22274
20: 348.62932: 0.148758 0.236232 0.140890 -2.45963 0.467458 -3.22516
21: 348.62094: 0.149100 0.236064 0.142779 -2.45980 0.475667 -3.22653
22: 348.61541: 0.145964 0.235440 0.148000 -2.46327 0.470978 -3.22776
23: 348.61273: 0.139750 0.235058 0.150849 -2.46421 0.475931 -3.22862
24: 348.60077: 0.136844 0.235397 0.157547 -2.46107 0.473210 -3.23013
25: 348.59434: 0.133357 0.233908 0.164716 -2.46229 0.474504 -3.22811
26: 348.58838: 0.128060 0.234947 0.171218 -2.46270 0.473326 -3.22830
27: 348.58516: 0.123314 0.235122 0.178312 -2.46234 0.473393 -3.22836
28: 348.58388: 0.119894 0.237515 0.185676 -2.46285 0.472785 -3.22922
29: 348.58175: 0.115664 0.235953 0.192852 -2.46184 0.472936 -3.22882
30: 348.58112: 0.116375 0.235245 0.192781 -2.46174 0.473003 -3.22860
31: 348.58089: 0.114832 0.235288 0.195777 -2.46201 0.472733 -3.22865
32: 348.58084: 0.113840 0.235423 0.197880 -2.46202 0.472782 -3.22866
33: 348.58084: 0.113738 0.235410 0.198166 -2.46201 0.472733 -3.22867
34: 348.58084: 0.113718 0.235407 0.198209 -2.46200 0.472738 -3.22867
Nonlinear mixed model fit by Laplace
Formula: conc ~ SSfol(Dose, Time, lKe, lKa, lCl) ~ (lKa + lCl | Subject)
Data: Theoph
Random effects:
Groups Name Variance Std.Dev. Corr
Subject 0.006640 0.081486
0.028715 0.169455 0.095
Residual 0.513461 0.716562
Number of obs: 132, groups: Subject, 12
Fixed effects:
lKe lKa lCl
-2.4620040 0.4727376 -3.2286810
lmer> (nm5 <- nlmer(conc ~ SSfol(Dose, Time,lKe, lKa, lCl) ~
(lKa|Subject) + (lCl|Subject),
lmer+ Theoph, start = c(lKe = -2.5, lKa = 0.5, lCl =
-3), verbose = 1))
0: 377.00821: 0.492366 0.492366 -2.50000 0.500000 -3.00000
1: 366.76107: 0.651153 0.445802 -2.37680 0.493764 -3.11563
2: 365.36949: 0.727845 0.339343 -2.56858 0.470938 -3.15375
3: 357.95634: 0.800556 0.235553 -2.43727 0.469676 -3.30431
4: 354.99052: 0.832260 0.259765 -2.48344 0.471084 -3.20395
5: 354.24411: 0.870423 0.236936 -2.44799 0.476074 -3.20614
6: 354.17301: 0.882142 0.234273 -2.47983 0.474481 -3.25200
7: 354.01600: 0.931094 0.245475 -2.46839 0.482925 -3.22876
8: 353.98864: 0.931074 0.239664 -2.46436 0.483016 -3.23136
9: 353.98458: 0.930993 0.237968 -2.46595 0.482944 -3.23014
10: 353.98400: 0.930867 0.237118 -2.46538 0.482925 -3.23051
11: 353.98394: 0.930160 0.236646 -2.46583 0.482637 -3.23007
12: 353.98374: 0.929216 0.236720 -2.46550 0.482309 -3.23037
13: 353.98370: 0.928140 0.236724 -2.46568 0.482320 -3.23030
14: 353.98368: 0.927745 0.236701 -2.46539 0.482224 -3.23029
15: 353.98368: 0.927700 0.236705 -2.46552 0.481755 -3.23040
16: 353.98368: 0.927689 0.236686 -2.46554 0.481775 -3.23036
17: 353.98368: 0.927672 0.236679 -2.46551 0.481820 -3.23037
18: 353.98367: 0.927645 0.236677 -2.46555 0.481928 -3.23037
19: 353.98367: 0.927612 0.236678 -2.46553 0.482015 -3.23039
20: 353.98367: 0.927527 0.236683 -2.46551 0.482012 -3.23035
21: 353.98367: 0.927478 0.236679 -2.46554 0.482090 -3.23035
22: 353.98367: 0.927453 0.236672 -2.46553 0.482134 -3.23035
23: 353.98367: 0.927456 0.236674 -2.46553 0.482133 -3.23035
Nonlinear mixed model fit by Laplace
Formula: conc ~ SSfol(Dose, Time, lKe, lKa, lCl) ~ (lKa | Subject) +
(lCl | Subject)
Data: Theoph
Random effects:
Groups Name Variance Std.Dev.
Subject 0.440915 0.66401
Subject 0.028712 0.16945
Residual 0.512588 0.71595
Number of obs: 132, groups: Subject, 12; Subject, 12
Fixed effects:
lKe lKa lCl
-2.4655280 0.4821327 -3.2303658
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