Dear John,
My dataset has a response variable with 6 levels, and
12 independent variables, 10 of them are continuous
variable, one is a categorical variable with 2 levels,
the other one is also a categorical variable with 4
levels. total 206 observations. I attached my dataset
with the email "sample.txt".
library(MASS)
library(nnet)
sample<-read.table("sample.txt",sep='\t',header=T,row.names=1)
wts2<-sample$wts
sample<-sample[,-4]
options(contrasts=c('contr.helmert','contr.poly'))
obj1<-multinom(class~.,sample,weights=wts2,maxit=1000)
options(contrasts=c('contr.treatment','contr.poly'))
obj2<-multinom(class~.,sample,weights=wts2,maxit=1000)
predict(obj1,type='probs')[1:5,]
predict(obj2,type='probs')[1:5,]
Interestingly, if I change the values of the variable
"bkgd" for 2 observations (from "a", to "f"), then I
can get convergence with helmert contrast, but still
not converged with treatment contrast:
sample$bkgd[201]<-'f'
sample$bkgd[205]<-'f'
options(contrasts=c('contr.helmert','contr.poly'))
obj1<-multinom(class~.,sample,weights=wts2,maxit=1000)
options(contrasts=c('contr.treatment','contr.poly'))
obj2<-multinom(class~.,sample,weights=wts2,maxit=1000)
predict(obj1,type='probs')[1:5,]
predict(obj2,type='probs')[1:5,]
appreciate any suggestions!
--- John Fox <[EMAIL PROTECTED]> wrote:
> Dear chip,
>
> > -----Original Message-----
> > From: [EMAIL PROTECTED]
> > [mailto:[EMAIL PROTECTED] On
> Behalf Of array chip
> > Sent: Thursday, April 14, 2005 1:00 PM
> > To: John Fox
> > Cc: [email protected]
> > Subject: RE: [R] multinom and contrasts
> >
> > Dear John,
> >
> > Thanks for the answer! In my own dataset, The
> > multinom() did not converge even after I had tried
> to
> > increase the maximum number of iteration (from
> default 100 to
> > 1000). In this situation, there is some bigger
> diffrenece in
> > fitted probabilities under different contrasts
> (e.g.
> > 0.9687817 vs. 0.9920816). My question is whether
> the analysis
> > (fitted probabilities) is still valid if it does
> not
> > converge? and what else can I try about it?
> >
>
> If multinom() doesn't converge to a stable solution
> after 1000 iterations,
> it's probably safe to say that the problem is
> ill-conditioned in some
> respect. Have you looked at the covariance matrix of
> the estimates?
>
> Regards,
> John
>
> > Thank you!
> >
> >
> >
> >
> > --- John Fox <[EMAIL PROTECTED]> wrote:
> > > Dear chip,
> > >
> > > The difference is small and is due to
> computational error.
> > >
> > > Your example:
> > >
> > > > max(abs(zz[1:10,] - yy[1:10,]))
> > > [1] 2.207080e-05
> > >
> > > Tightening the convergence tolerance in
> multinom() eliminates the
> > > difference:
> > >
> > > >
> > >
> options(contrasts=c('contr.treatment','contr.poly'))
> > > >
> > >
> >
>
xx<-multinom(Type~Infl+Cont,data=housing[-c(1,10,11,22,25,30),],
> > > reltol=1.0e-12)
> > > # weights: 20 (12 variable)
> > > initial value 91.495428
> > > iter 10 value 91.124526
> > > final value 91.124523
> > > converged
> > > > yy<-predict(xx,type='probs')
> > > >
> options(contrasts=c('contr.helmert','contr.poly'))
> > > >
> > >
> >
>
xx<-multinom(Type~Infl+Cont,data=housing[-c(1,10,11,22,25,30),],
> > > reltol=1.0e-12)
> > > # weights: 20 (12 variable)
> > > initial value 91.495428
> > > iter 10 value 91.125287
> > > iter 20 value 91.124523
> > > iter 20 value 91.124523
> > > iter 20 value 91.124523
> > > final value 91.124523
> > > converged
> > > > zz<-predict(xx,type='probs')
> > > > max(abs(zz[1:10,] - yy[1:10,]))
> > > [1] 1.530021e-08
> > >
> > > I hope this helps,
> > > John
> > >
> > > --------------------------------
> > > John Fox
> > > Department of Sociology
> > > McMaster University
> > > Hamilton, Ontario
> > > Canada L8S 4M4
> > > 905-525-9140x23604
> > > http://socserv.mcmaster.ca/jfox
> > > --------------------------------
> > >
> > > > -----Original Message-----
> > > > From: [EMAIL PROTECTED]
> > > > [mailto:[EMAIL PROTECTED] On
> > > Behalf Of array chip
> > > > Sent: Wednesday, April 13, 2005 6:26 PM
> > > > To: [email protected]
> > > > Subject: [R] multinom and contrasts
> > > >
> > > > Hi,
> > > >
> > > > I found that using different contrasts (e.g.
> > > > contr.helmert vs. contr.treatment) will
> generate
> > > different
> > > > fitted probabilities from multinomial logistic
> > > regression
> > > > using multinom(); while the fitted
> probabilities
> > > from binary
> > > > logistic regression seem to be the same. Why
> is
> > > that? and for
> > > > multinomial logisitc regression, what contrast
> > > should be
> > > > used? I guess it's helmert?
> > > >
> > > > here is an example script:
> > > >
> > > > library(MASS)
> > > > library(nnet)
> > > >
> > > > #### multinomial logistic
> > > >
> > >
> options(contrasts=c('contr.treatment','contr.poly'))
> > > >
> > >
> >
>
xx<-multinom(Type~Infl+Cont,data=housing[-c(1,10,11,22,25,30),])
> > > > yy<-predict(xx,type='probs')
> > > > yy[1:10,]
> > > >
> > > >
> options(contrasts=c('contr.helmert','contr.poly'))
> > > >
> > >
> >
>
xx<-multinom(Type~Infl+Cont,data=housing[-c(1,10,11,22,25,30),])
> > > > zz<-predict(xx,type='probs')
> > > > zz[1:10,]
> > > >
> > > >
> > > > ##### binary logistic
> > > >
> > >
> options(contrasts=c('contr.treatment','contr.poly'))
> > > >
> > >
> >
>
obj.glm<-glm(Cont~Infl+Type,family='binomial',data=housing[-c(
> > > 1,10,11,22,25,30),])
> > > > yy<-predict(xx,type='response')
> > > >
> > > >
> options(contrasts=c('contr.helmert','contr.poly'))
> > > >
> > >
> >
>
obj.glm<-glm(Cont~Infl+Type,family='binomial',data=housing[-c(
> > > 1,10,11,22,25,30),])
> > > > zz<-predict(xx,type='response')
> > > >
> > > > Thanks
> > > >
> > > > ______________________________________________
> > > > [email protected] mailing list
> > > > https://stat.ethz.ch/mailman/listinfo/r-help
> > > > PLEASE do read the posting guide!
> > > > http://www.R-project.org/posting-guide.html
> > >
> > >
> >
> > ______________________________________________
> > [email protected] mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide!
> > http://www.R-project.org/posting-guide.html
>
>
__________________________________
sample class sex bkgd wts v1 v2 v3 v4 v5
v6 v7 v8 v9 v10
1 a f uk 0.008297258 19.04472 19.04472
15.86904 19.04472 7.178546 14.03481 18.04475
14.73449 19.04472 18.04475
2 a f uk 0.008297258 16.90796 15.06369
15.90808 16.90796 9.971099 16.90796 7.580712
16.90796 8.688114 15.04616
3 a m uk 0.008297258 17.76695 13.54463
16.76702 17.76695 9.933965 17.76695 5.744463
15.34231 17.76695 16.76702
4 a m uk 0.008297258 17.80119 19.83282
15.76018 19.83282 16.91393 19.83282 13.85726
14.37534 14.78603 18.83283
5 a m uk 0.008297258 18.19009 20.76601
10.51376 18.84936 4.336975 8.054065 18.86812
13.30747 17.84244 13.70478
6 a m uk 0.008297258 14.95027 18.59327
13.64135 18.59327 10.89967 15.7 17.59331
18.59327 11.23647 14.23134
7 a m uk 0.008297258 16.27883 16.27883
15.27901 16.27883 12.27462 11.9437 6.073054
11.96241 16.27883 15.27901
8 a m uk 0.008297258 17.10468 17.10468
8.30414 17.10468 3.702566 5.610083 16.10478
10.88243 17.10468 10.75839
9 a m uk 0.008297258 12.14245 19.7965
11.82096 19.7965 14.34383 13.13702 18.79651
15.06788 14.49629 8.169033
10 a m uk 0.008297258 16.83262 16.83262
10.98971 16.83262 3.990028 7.214775 15.83274
13.85126 16.83262 14.81813
11 a f uk 0.008297258 15.15698 19.84287
9.883373 19.84287 4.062335 5.543951 18.84289
13.5462 14.26999 10.1136
12 a m uk 0.008297258 17.41835 17.41835
16.41844 17.41835 12.76132 17.41835 5.795233
12.36125 16.14529 13.67857
13 a m uk 0.008297258 13.29703 17.71998
16.72004 17.71998 13.10685 17.71998 5.468795
15.44379 11.83178 11.85085
14 a m uk 0.008297258 15.82607 18.58887
16.69162 18.58887 12.40997 18.58887 4.768042
14.30013 6.790248 12.36805
15 a f uk 0.008297258 16.33669 20.79222
8.717149 20.79222 3.672298 6.239112 17.22278
12.16464 18.55192 10.07866
16 a m uk 0.008297258 16.9932 16.9932 11.86621
16.9932 12.86455 9.111293 15.62647 12.08379
10.79863 12.1129
17 a f uk 0.008297258 12.29573 18.63263
12.41431 18.63263 5.335175 5.951081 17.63267
12.0974 18.63263 10.44992
18 a f uk 0.008297258 16.47659 16.47659
11.57741 16.47659 4.918529 7.192721 15.47675
14.76269 16.47659 13.59735
19 a f f 0.008297258 16.85668 19.96856
10.7923 19.96856 16.21171 8.302365 18.96858 9.15754
12.57342 10.61172
20 a m uk 0.008297258 17.32721 17.03846
17.0753 17.32721 13.71286 17.32721 17.32721
15.49237 17.32721 12.50622
21 a f uk 0.008297258 15.70945 20.56752
10.50372 20.13379 12.24092 9.50097 20.56752
15.37041 12.54465 12.23782
22 a m uk 0.008297258 15.62071 15.62071
13.36193 15.62071 3.569063 9.315931 15.62071
12.88391 15.15205 15.46448
23 a f uk 0.008297258 16.72489 16.72489
11.0507 16.72489 4.734268 11.29278 16.72489
16.25853 16.72489 11.2044
24 a m uk 0.008297258 15.23403 19.21367
10.59019 19.21367 11.24257 9.072279 18.89542
15.11491 11.82384 13.56817
25 a f uk 0.008297258 16.59134 16.59134
15.1489 16.59134 9.519951 13.91706 16.00523
11.02024 15.10438 14.46948
26 b f uk 0.005772006 13.97664 17.61178
10.19103 17.61178 12.94985 17.61178 13.93402
11.2029 6.200198 13.07556
27 b m uk 0.005772006 15.18097 15.18097
13.80335 15.18097 12.99142 15.18097 12.71298
12.87276 11.62028 15.09058
28 b m uk 0.005772006 18.12814 19.90946
12.1951 17.75636 13.97289 19.15999 13.70799
18.81477 9 13.70005
29 b f uk 0.005772006 14.66449 16.88023
14.72744 16.88023 16.88023 16.88023 13.70659
12.59085 12.86337 16.26697
30 b f uk 0.005772006 16.63918 16.982
10.15189 14.60469 12.4889 16.982 15.85343 9.634332
6.489862 11.80008
31 b m uk 0.005772006 14.06745 17.47725
11.11697 14.78366 10.9068 13.62444 16.12358
8.751102 7.999291 12.32946
32 b m uk 0.005772006 9.023867 18.52602
15.40251 17.58645 12.31045 18.28202 18.52602
15.29716 4.613386 6.457461
33 b f uk 0.005772006 10.88312 19.09323
8.710526 17.22736 12.32276 14.16131 17.66152
13.08787 9.593295 7.289902
34 b m uk 0.005772006 14.71518 19.60225
9.791677 18.02487 13.67973 17.28676 10.83714
12.27599 11.31451 16.72101
35 b m uk 0.005772006 11.8743 18.80156
10.41827 17.3091 13.48478 18.91988 16.53553
14.18178 6.102764 9.765983
36 b m uk 0.005772006 9.251961 14.06166
11.68759 18.99687 12.15485 18.99687 17.62109
15.04187 16.41189 11.06143
37 b m uk 0.005772006 10.77104 19.03226
11.62019 12.7084 14.50394 13.79427 10.2538 14.25789
14.40289 16.10839
38 b m uk 0.005772006 16.475 20.28859
11.70615 18.07253 12.6943 20.28859 11.83247
15.81084 6.19423 12.49606
39 b f uk 0.005772006 9.570085 16.91038
10.73726 13.77976 15.08654 16.91038 16.91038
16.91038 6.964057 13.43508
40 b f uk 0.005772006 15.84286 20.38897
12.16168 20.19348 15.45095 19.9117 14.4589 11.63776
6.957877 13.49832
41 b m uk 0.005772006 13.13849 17.52612
12.24296 17.52612 14.93202 17.52612 11.9617
9.517386 8.227286 15.93525
42 b f a 0.005772006 16.81302 17.15827
8.39735 12.79796 3.788864 7.515404 10.13464
14.01964 7.324637 12.23765
43 b f uk 0.005772006 16.48097 18.67843
11.06133 18.53315 13.92307 18.67843 17.85734
15.15229 6.799235 9.090954
44 b m uk 0.005772006 14.39199 21.21674
12.13853 17.5258 16.07249 14.42395 9.572172
12.37167 6.822834 14.26482
45 b m uk 0.005772006 16.13721 19.77461
15.18544 19.95126 14.93958 19.87399 12.26347
8.947859 12.91003 13.31446
46 b m uk 0.005772006 12.58618 15.68334
15.3004 15.68334 11.85851 15.68334 7.41904 15.68334
7.237328 15.146
47 b m uk 0.005772006 15.30124 15.30124
13.37807 15.30124 12.54366 12.44942 8.960764
14.41137 4.302645 11.7006
48 b f uk 0.005772006 15.99117 18.26286
11.12763 16.87763 14.80153 18.09466 20.39867
15.7562 11.28632 15.59845
49 b m uk 0.005772006 16.16219 16.16219
16.05967 13.21236 15.20422 16.16219 16.10804
15.37534 12.5334 12.56376
50 b m uk 0.005772006 15.4826 16.3882 13.8934
15.45341 14.88868 14.11555 20.02541 9.856336
5.311844 10.92895
51 b f uk 0.005772006 10.29412 20.16092
12.03374 15.95406 15.91354 20.16092 20.16092
13.86876 5.31528 7.020118
52 b m uk 0.005772006 16.08142 17.33302
12.40182 17.33302 14.49425 17.33302 15.72702
15.8596 6.630614 14.42785
53 b m uk 0.005772006 15.39923 18.15249
12.43441 18.15249 16.37116 18.15249 18.15249
8.749028 17.19668 12.7652
54 b m uk 0.005772006 16.16528 16.84297
13.24135 16.84297 14.21664 16.84297 16.84297
8.341829 10.7173 11.19625
55 b m uk 0.005772006 11.33668 20.36364
12.72925 17.03116 16.23343 20.13985 11.22305
16.17193 5.202193 9.512463
56 b f uk 0.005772006 15.96558 18.90113
11.48566 18.90113 14.39105 17.42177 14.03426
11.25117 7.748889 7.875705
57 b m uk 0.005772006 15.5008 20.29624
14.82075 20.12502 16.06476 20.29624 7.583192
13.8964 7.259166 8.38886
58 b f uk 0.005772006 18.40897 18.40897
15.61394 18.40897 14.83036 16.84241 18.01554
15.32335 7.0197 8.694882
59 b m uk 0.005772006 15.98768 19.71666
11.85256 18.82948 17.33911 19.71666 19.71666
12.57806 7.187513 8.696203
60 b f uk 0.005772006 10.60757 19.12452
10.93998 19.12452 16.41793 19.12452 15.53748
14.93226 18.12645 8.981042
61 b f uk 0.005772006 10.17433 18.82357
13.90919 17.97518 16.08361 18.82357 13.73977
8.357278 9.951942 9.698362
62 b m uk 0.005772006 15.26588 19.71194
13.16427 19.71194 17.75207 17.8434 12.84484
9.854448 9.744693 12.39929
63 b m uk 0.005772006 13.99867 19.88128
19.61754 19.91557 15.78354 19.96602 19.96602
11.98126 18.47239 5.852174
64 b f uk 0.005772006 16.18216 16.63926
10.09553 17.20193 14.816 18.81545 20.23256
11.92017 13.8167 10.74317
65 b m uk 0.005772006 9.796737 19.47366
15.24231 19.47366 15.89083 19.40495 18.9123
13.87504 11.34207 7.684333
66 b f uk 0.005772006 17.69846 19.33468
13.14969 17.22946 17.2036 19.33468 19.08929
13.74165 7.919697 8.111683
67 c f uk 0.003246753 9.443346 18.11216
13.47627 17.62306 14.75291 20.1352 17.76303 20.1352
20.1352 13.56752
68 c m a 0.003246753 7.60292 21.5161 15.25623
18.24048 3.920972 8.84146 14.02793 15.0044 21.5161 13.98864
69 c f uk 0.003246753 7.525356 22.58878
12.46233 16.38371 14.82679 22.58878 15.80563
15.10319 22.58878 16.07823
70 c f uk 0.003246753 9.414247 8.184074
13.49119 14.04545 14.20021 18.61331 17.61335
18.61331 18.61331 14.99085
71 c m uk 0.003246753 7.542121 10.66081
12.95027 13.44963 13.00122 18.93972 12.47208
12.66965 18.93972 13.96344
72 c m uk 0.003246753 9.314504 21.52367
16.6599 15.11493 13.86421 21.52367 14.53577 17.8215
21.52367 14.62346
73 c f uk 0.003246753 6.360998 17.47988
13.84491 16.9613 14.10849 19.90728 16.1586 15.31296
19.90728 15.47898
74 c m uk 0.003246753 9.754932 18.21408
11.15589 14.70663 14.76661 18.21408 11.3345
14.31818 18.21408 13.82726
75 c m uk 0.003246753 9.324921 19.17362
16.94829 19.17362 15.49851 19.17362 18.17364
19.17362 19.17362 18.17364
76 c m uk 0.003246753 7.836779 20.85398
12.54097 18.45158 13.47948 18.01471 19.85399
20.85398 13.5426 10.11275
77 c m uk 0.003246753 8.188882 20.41102
15.46259 15.87985 15.96034 20.41102 13.31929
14.72443 20.41102 13.1754
78 c f uk 0.003246753 10.10567 18.16197
18.71686 19.71684 15.32771 19.71684 13.30421
10.38928 19.71684 14.98304
79 c f uk 0.003246753 6.983307 20.04566
12.6247 17.37969 14.78694 20.04566 9.955649
13.17532 20.04566 8.396564
80 c m uk 0.003246753 7.130417 13.46595
15.98486 19.76544 15.0038 19.76544 18.6018 12.42082
15.6377 11.38557
81 c f a 0.003246753 6.978853 19.97976
14.20264 19.97976 5.997562 10.81952 17.84641
12.24549 19.97976 15.35688
82 c f uk 0.003246753 7.535644 20.97992
13.45741 17.17522 16.84708 20.97992 14.90624
12.51926 20.97992 11.12932
83 c f f 0.003246753 11.84268 20.48416
11.92454 15.43138 15.04724 20.48416 19.25814
8.457197 9.125998 7.088488
84 c f a 0.003246753 15.01553 17.17952
13.87211 15.54179 12.63471 18.08498 18.74425
5.55847 19.74424 11.17968
85 c m uk 0.003246753 9.21438 16.53553
15.12414 16.53553 14.42293 16.53553 15.53568
10.40759 16.53553 13.68569
86 c f uk 0.003246753 6.451176 17.70058
16.70065 14.37182 14.34909 17.70058 11.12898
14.29423 9.960127 11.26636
87 c f uk 0.003246753 8.79245 16.3495 15.34967
16.3495 14.6592 16.3495 11.86427 16.3495 16.3495 13.15891
88 c m uk 0.003246753 8.080361 19.6627
15.81798 19.6627 16.2289 19.6627 12.69531 15.37507 19.6627
8.925245
89 c m uk 0.003246753 6.655329 20.29249
11.10626 20.29249 11.19677 20.29249 19.2925
10.38089 13.03523 10.90329
90 c m uk 0.003246753 8.64289 17.54906
16.54913 12.57234 13.86973 17.54906 8.502753
11.62791 17.54906 11.47
91 c m uk 0.003246753 8.304915 19.98169
12.68798 17.56292 16.21673 16.10245 16.87598
12.65901 19.98169 8.203063
92 c f uk 0.003246753 7.662408 15.94369
14.94392 15.94369 15.94369 15.94369 10.15444
12.34352 15.94369 12.05303
93 c m uk 0.003246753 8.177233 17.46916
16.46924 15.45591 10.68326 8.017774 15.95208
10.27389 15.01946 14.51691
94 c m uk 0.003246753 6.680182 17.03292
12.03616 14.05249 14.64084 17.03292 13.83395
17.03292 14.18196 12.38324
95 c f uk 0.003246753 8.186086 18.57753
15.24061 14.16397 16.5893 18.57753 13.73877
12.74243 9.827667 10.69198
96 c f uk 0.003246753 8.577452 16.46428
12.82075 12.79295 12.78076 16.46428 15.46444
14.3175 16.46428 10.24034
97 c f uk 0.003246753 8.345212 17.8225
13.87337 17.8225 13.67425 13.43626 12.35784
10.68919 17.8225 16.3972
98 d f a 0.001082251 16.5028 19.52847
12.50123 19.52847 3.7008 10.96342 10.08577 15.5778
13.47766 13.88017
99 d f uk 0.001082251 15.31145 14.507
8.699603 19.09358 13.51945 19.09358 14.30743
19.09358 19.09358 18.09361
100 d f uk 0.001082251 18.58207 16.92002
5.690195 20.25405 12.23465 20.25405 19.25406
20.25405 17.02858 17.47984
101 d f uk 0.001082251 15.04715 4.809195
11.01907 20.79889 13.15931 19.67613 10.69306
16.54484 13.27312 18.96375
102 d f uk 0.001082251 18.38653 10.09539
8.913216 20.59283 11.41535 13.23227 19.59284
15.89595 20.59283 16.74383
103 d f uk 0.001082251 18.19158 6.483819
7.809166 21.3604 13.31897 21.3604 20.36041 21.3604
19.31149 14.35019
104 d f uk 0.001082251 15.63278 15.57834
7.103375 18.04317 14.08714 18.04317 13.33736
13.59917 13.98539 17.04323
105 d f f 0.001082251 15.73415 3.729024
5.000463 10.16948 14.72392 21.02839 20.02839
8.791972 14.87173 12.79048
106 d f f 0.001082251 15.36538 4.576747
6.55979 20.33191 15.8166 20.33191 19.33192 8.244799
7.832203 14.4098
107 d f uk 0.001082251 16.47582 8.693146
5.986334 17.68436 14.03669 17.7902 20.93872
9.611697 11.25831 9.057905
108 d f a 0.001082251 14.86838 15.94835
14.57347 18.29744 4.392416 9.610381 12.27258
12.28569 12.9133 4.14991
109 d f f 0.001082251 15.6187 6.674266
7.347359 19.39506 13.5373 17.17666 18.39508
6.781846 9.873021 15.00886
110 d f f 0.001082251 16.59957 8.715214
8.62492 14.28147 14.64913 20.64706 19.64707
6.952226 9.720664 12.35284
111 d f uk 0.001082251 14.96533 3.78174
8.212472 10.23557 16.44652 20.81496 19.58315
9.419028 14.29723 11.76647
112 d f f 0.001082251 19.5014 6.87415 7.819955
19.5014 15.08339 19.5014 18.50142 7.741215 15.40485
16.41076
113 d f f 0.001082251 17.42264 6.947724
8.076092 13.90663 14.949 19.50194 18.50196
8.831596 14.95316 13.59443
114 d f f 0.001082251 16.5456 3.806555
7.659662 13.06305 16.6811 19.73397 18.73398
6.646338 10.65326 15.35624
115 d f f 0.001082251 16.21146 3.681997
5.745054 15.66603 13.79984 19.50528 16.70967
7.383984 11.40589 11.98369
116 d f f 0.001082251 18.17195 7.160575
8.494647 14.74378 13.5162 18.17195 17.17199
7.297585 12.50175 14.57161
117 d f f 0.001082251 8.353964 16.01125
14.18937 17.92177 17.92177 17.92177 16.73819
8.641204 17.92177 12.67171
118 d f f 0.001082251 16.79675 3.44907
6.855023 13.99884 15.18634 19.91946 18.91948
7.534573 18.13416 14.4924
119 d f f 0.001082251 16.09902 11.35213
9.084248 19.88747 15.29297 19.88747 18.88748
5.575244 15.48529 9.893932
120 d f f 0.001082251 17.27609 9.060046
8.08725 18.74808 14.39463 18.74808 17.74811
6.967318 18.74808 14.4221
121 d f f 0.001082251 17.74729 4.07539 7.27107
17.74729 17.74729 17.74729 16.74735 10.42872
12.22295 14.88435
122 d f f 0.001082251 16.05136 3.922655
5.130967 14.06163 14.30585 20.08228 19.08229
9.310851 13.16989 15.22978
123 d f f 0.001082251 16.4143 17.6445 6.570568
11.89738 14.25298 18.52543 20.17783 11.28958
9.21848 11.29628
124 d f f 0.001082251 16.49753 3.543793
6.84077 19.06891 15.30704 19.06891 18.06894
6.749843 16.16811 17.69686
125 d f a 0.001082251 14.11004 5.412009
9.237217 19.25125 5.46951 10.50206 10.23127
10.46942 13.56566 7.703765
126 d f a 0.001082251 12.79314 5.336332
7.272206 18.45158 4.533847 8.969061 17.45162
12.78744 9.133678 11.98615
127 d f f 0.001082251 6.370428 20.71658
12.64609 15.30309 15.33113 20.71658 19.62445
7.6428 15.01053 12.35436
128 d f f 0.001082251 15.23938 4.260658
6.840384 17.81578 14.63676 20.24523 19.24524
8.018308 7.897332 14.89017
129 d f f 0.001082251 16.25297 4.60779
6.101993 14.02432 15.84135 20.90136 19.90137
6.99568 12.9172 15.34301
130 d f f 0.001082251 17.20637 4.84246
5.910276 17.23524 15.52939 20.50941 20.50941
7.259907 13.87992 17.03434
131 e m uk 0.000721501 14.98387 16.29623
4.846064 3.363969 14.7292 19.62162 13.99867
14.22776 9.16591 13.76378
132 e m uk 0.000721501 15.08906 16.08664
4.85986 3.380756 15.75712 18.2188 16.78587 18.2188
9.035402 11.71533
133 e m uk 0.000721501 14.23885 19.48381
5.135897 3.456389 14.73017 19.48381 16.2273
12.21813 9.427361 13.34611
134 e m uk 0.000721501 14.60512 18.39708
5.205959 3.396924 14.4612 15.0661 17.39713 11.557
9.000008 8.987012
135 e m uk 0.000721501 14.56196 15.68991
5.14841 3.37855 15.12351 12.48668 13.34215 10.7907
5.132524 10.1044
136 e m uk 0.000721501 16.64116 18.5533
4.565611 3.356968 14.23797 18.5533 17.15432
13.04824 13.50935 12.87322
137 e m uk 0.000721501 16.61819 18.85197
5.001413 3.385148 14.02929 18.85197 14.25981
15.16512 12.86807 8.363665
138 e m uk 0.000721501 15.41928 18.34464
4.519437 3.34707 13.75357 18.34464 17.34468
15.01872 10.97505 7.83686
139 e m uk 0.000721501 15.43732 19.27787
5.842953 3.430765 14.65233 19.27787 13.74963
11.94557 7.109612 11.45862
140 e m uk 0.000721501 13.64986 19.86848
4.852243 3.395105 14.28768 19.86848 15.32576
17.50791 11.79931 9.197711
141 e m uk 0.000721501 15.8928 19.86058
5.597184 3.411603 18.12022 12.76548 18.86059
12.74094 9.902369 6.327679
142 e m uk 0.000721501 16.08312 18.7541
5.369482 3.378645 15.99189 18.7541 17.75413 18.7541
15.39699 13.2783
143 e m uk 0.000721501 14.69797 20.28833
5.044494 3.360856 13.95116 20.28833 19.28834
13.54702 5.534511 10.65468
144 e m uk 0.000721501 14.63845 19.27016
4.589272 3.350127 15.45512 19.27016 16.24278
13.50518 12.07869 12.45855
145 e m uk 0.000721501 14.69906 20.16103
5.119965 3.403803 15.23221 9.960287 16.05247
12.90503 12.94157 6.488537
146 e m uk 0.000721501 15.62488 19.19539
4.503286 3.356612 16.83588 19.19539 14.11887
12.88724 11.25476 7.758865
147 e m uk 0.000721501 15.25086 18.68674
4.793845 3.345574 18.68674 10.38632 16.32224
10.80285 5.537264 5.596134
148 e m uk 0.000721501 14.94879 14.75613
4.633708 3.366012 16.41349 19.51919 16.6728
16.45927 10.81037 10.33797
149 e m uk 0.000721501 16.23019 16.23
5.361942 3.4 14.07084 16.35 16.23 17.81 16.23 12.71
150 f f uk 0.001443001 18.93482 15.06068
9.472486 18.93482 11.02462 11.65361 17.93485
5.464129 15.22974 16.42301
151 f f c 0.001443001 15.18434 15.71677
13.05015 20.06403 12.77767 16.78854 19.06404
5.752287 20.06403 16.82065
152 f f uk 0.001443001 16.52223 18.96315
17.96317 18.96315 15.60871 18.96315 17.96317
8.74487 15.32282 17.96317
153 f f uk 0.001443001 11.19445 20.79157
11.55399 18.29305 13.12066 20.79157 19.79157
6.251829 20.79157 16.84205
154 f f uk 0.001443001 16.86733 19.08434
16.79819 19.08434 14.90113 19.08434 18.08436
9.923692 19.08434 18.08436
155 f f uk 0.001443001 16.91705 19.91877
14.27896 18.62696 13.34829 19.91877 16.78866
8.072026 15.30424 16.4934
156 f f c 0.001443001 16.24523 19.84908
11.99309 19.84908 15.48313 19.84908 18.05542
6.265361 19.84908 14.77038
157 f f uk 0.001443001 13.96114 15.59276
15.96202 15.10756 12.83886 20.05061 18.28116
5.680101 18.32469 14.80301
158 f f uk 0.001443001 17.78557 16.20865
8.233437 18.90829 14.63434 21.715 18.05479
5.804084 16.01247 14.34449
159 f f uk 0.001443001 13.93784 14.31135
8.420117 12.44432 15.94761 19.10231 15.59901
7.817195 16.32061 7.481692
160 f f uk 0.001443001 17.43794 14.76389
11.77344 20.65234 13.96198 20.65234 19.65234
6.960799 17.42322 14.30507
161 f f uk 0.001443001 17.45261 12.10964
7.836801 19.96305 12.08647 19.96305 18.56042
5.049859 17.02038 14.56612
162 f f uk 0.001443001 13.25875 3.637332
5.541177 16.66706 14.53575 12.45895 19.53347
11.04571 10.67302 10.81376
163 f f uk 0.001443001 16.58887 19.40516
14.22473 14.19594 14.14168 15.71497 17.20495
4.981759 19.5625 16.12642
164 f f uk 0.001443001 18.68537 15.62789
11.96859 21.85634 15.86901 21.85634 20.85634
9.585069 18.01844 11.73879
165 f f uk 0.001443001 17.46057 12.34245
13.93374 21.07973 14.44233 21.07973 15.35807
5.772433 11.12186 12.84434
166 f f uk 0.001443001 16.07459 13.60523
9.288766 19.19388 13.19374 19.19388 17.79821
5.86084 12.97269 14.87415
167 f f uk 0.001443001 17.49457 21.33565
12.30464 16.98912 14.80522 21.33565 20.13529
6.784472 16.42099 15.6984
168 f f uk 0.001443001 18.9138 16.13187
16.58814 12.84674 13.07314 11.36321 9.967642
10.42023 9.17325 10.8909
169 f f uk 0.001443001 16.70502 13.59217
10.27153 13.59051 13.75114 19.9255 18.92552
5.524162 14.92324 15.86987
170 f f a 0.001443001 14.19942 16.69677
7.500619 18.67725 9.839796 10.20425 11.10115
13.36316 6.041942 9.781457
171 f f uk 0.001443001 16.05594 3.859549
8.215248 8.369811 15.51753 18.18292 8.902281
13.40934 14.08177 13.95399
172 f f uk 0.001443001 15.94099 18.75019
17.02678 15.98358 13.71896 18.75019 14.65078
6.181292 18.75019 12.28743
173 f f uk 0.001443001 10.35122 21.83626
8.323749 10.59381 16.7785 21.83626 16.12457
8.547815 12.4972 12.84462
174 f f uk 0.001443001 18.78316 14.63081
11.4361 20.63647 12.37279 20.63647 16.69098
6.189123 16.84129 13.14508
175 f f uk 0.001443001 15.97827 12.12942
8.911746 19.08654 11.69486 19.08654 17.93906
5.240442 15.91661 13.45902
176 f f uk 0.001443001 16.41512 18.95907
16.09808 17.0298 14.32881 18.95907 17.9591 7.292677
18.95907 13.66371
177 f f uk 0.001443001 17.03701 15.81308
11.07242 20.57781 13.94323 20.57781 18.7621
5.919108 14.72834 13.72965
178 f f uk 0.001443001 16.10181 16.44533
13.94578 18.00915 11.42488 18.00915 15.73846
6.32068 9.278421 14.02425
179 f f uk 0.001443001 16.62347 17.17948
11.85938 18.76861 14.4213 18.76861 14.51647
8.345467 18.76861 12.88049
180 f f uk 0.001443001 17.37967 14.8313
11.43392 18.97532 13.81401 21.01476 16.60145
6.958171 13.76008 11.22648
181 f f uk 0.001443001 14.88318 20.46502
12.40828 17.15243 13.35891 16.17406 19.46503
8.7335 12.09762 15.69051
182 f f uk 0.001443001 16.9576 11.85327
14.20329 15.11787 14.36121 18.39324 12.75581
7.718279 15.26106 15.48501
183 f f c 0.001443001 9.857473 19.48821
11.26209 13.44403 14.04766 19.48821 17.70405
5.349663 18.08218 15.4108
184 g m a 0.015512266 15.59977 18.05342
13.61004 18.05342 14.13485 18.05342 7.724268
15.31586 18.05342 17.05347
185 g m uk 0.015512266 15.06348 21.69419
18.42057 21.69419 13.68216 18.89551 20.6942
17.98755 21.69419 18.19784
186 g m uk 0.015512266 15.6071 20.49882
19.49883 20.49882 12.23962 18.54236 8.372173
15.31494 20.49882 12.93382
187 g f uk 0.015512266 16.72301 18.03345
15.88055 18.03345 12.64184 13.99314 18.03345
13.9495 18.03345 13.60404
188 g m a 0.015512266 17.23546 19.93053
18.93054 19.93053 5.263118 11.38754 18.93054
17.87834 17.65817 18.93054
189 g f uk 0.015512266 13.22848 19.69495
13.35452 19.69495 13.29535 19.69495 18.69496
19.69495 19.69495 11.90249
190 g f uk 0.015512266 15.2177 18.34245
17.01974 18.34245 14.82707 18.34245 11.04946
10.67752 18.34245 17.34249
191 g f f 0.015512266 16.66004 19.00857
13.44218 15.17912 13.20143 19.00857 18.65363
9.001643 7.281456 13.92505
192 g f f 0.015512266 9.184064 20.42593
15.17502 14.99434 12.77405 19.20457 13.43731
12.005 10.70005 10.32349
193 g f f 0.015512266 9.509863 20.28146
16.31676 17.66582 13.65649 20.28146 8.197611
12.45318 20.18952 13.6287
194 g m uk 0.015512266 10.71109 21.46639
11.08973 21.46639 13.04486 21.46639 14.77621
18.09663 21.46639 10.79776
195 g m uk 0.015512266 10.53458 17.36017
15.08472 17.36017 14.78826 17.36017 15.81062
17.36017 17.36017 14.75894
196 g f a 0.015512266 16.95631 21.02553
8.12126 20.39257 4.033282 7.243288 21.02553
9.764743 9.957615 17.95086
197 g f f 0.015512266 13.33134 19.3105
15.12361 17.05739 12.75544 19.55525 18.93938
7.978972 7.959061 16.96414
198 g m a 0.015512266 17.45392 20.39022
18.28444 20.39022 5.786533 11.30957 20.36234
15.00883 17.13787 9.691086
199 g f uk 0.015512266 15.44437 15.14665
17.80186 18.80183 13.13257 18.80183 17.4682
8.662849 18.80183 17.80186
200 g m uk 0.015512266 18.6126 19.31185 17.9296
18.18465 13.38705 18.25151 19.5074 18.56573
19.30054 8.785971
201 g m a 0.015512266 14.59621 19.31899
17.61284 18.0128 12.14914 19.01323 19.31899
14.52241 17.17985 18.76792
202 g f uk 0.015512266 18.58369 18.87781
18.87781 18.19909 14.0331 18.87781 18.87781
11.90628 18.87781 10.8255
203 g f uk 0.015512266 16.03607 20.51338
18.09249 20.51338 14.34255 20.2414 20.51338
12.46368 17.35791 13.16367
204 g f uk 0.015512266 17.79669 20.02274
16.93237 19.83503 13.79137 14.57115 20.02274
13.89721 19.52417 10.86221
205 g f a 0.015512266 17.59605 17.94264
17.94264 17.94264 6.830621 12.53348 17.94264
10.00496 16.60827 14.56825
206 g m uk 0.015512266 16.61251 16.61251
16.61251 16.61251 16.61251 16.61251 16.50754
11.21726 15.33446 15.33446
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