Elastic net model paths for some generalized linear models
glmnet-package.RdThis package fits lasso and elastic-net model paths for regression, logistic and multinomial regression using coordinate descent. The algorithm is extremely fast, and exploits sparsity in the input x matrix where it exists. A variety of predictions can be made from the fitted models.
Details
| Package: | glmnet |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2008-05-14 |
| License: | What license is it under? |
Very simple to use. Accepts x,y data for regression models, and
produces the regularization path over a grid of values for the tuning
parameter lambda. Only 5 functions: glmnetpredict.glmnetplot.glmnetprint.glmnetcoef.glmnet
References
Friedman, J., Hastie, T. and Tibshirani, R. (2008)
Regularization Paths for Generalized Linear Models via Coordinate
Descent (2010), Journal of Statistical Software, Vol. 33(1), 1-22,
doi:10.18637/jss.v033.i01
.
Simon, N., Friedman, J., Hastie, T. and Tibshirani, R. (2011)
Regularization Paths for Cox's Proportional
Hazards Model via Coordinate Descent, Journal of Statistical Software, Vol.
39(5), 1-13,
doi:10.18637/jss.v039.i05
.
Tibshirani,Robert, Bien, J., Friedman, J., Hastie, T.,Simon, N.,Taylor, J. and
Tibshirani, Ryan. (2012) Strong Rules for Discarding Predictors in
Lasso-type Problems, JRSSB, Vol. 74(2), 245-266,
https://arxiv.org/abs/1011.2234.
Hastie, T., Tibshirani, Robert and Tibshirani, Ryan (2020) Best Subset,
Forward Stepwise or Lasso? Analysis and Recommendations Based on Extensive Comparisons,
Statist. Sc. Vol. 35(4), 579-592,
https://arxiv.org/abs/1707.08692.
Glmnet webpage with four vignettes: https://glmnet.stanford.edu.
Examples
x = matrix(rnorm(100 * 20), 100, 20)
y = rnorm(100)
g2 = sample(1:2, 100, replace = TRUE)
g4 = sample(1:4, 100, replace = TRUE)
fit1 = glmnet(x, y)
predict(fit1, newx = x[1:5, ], s = c(0.01, 0.005))
#> s1 s2
#> [1,] 0.8990504 0.9517110
#> [2,] 0.1207432 0.1060893
#> [3,] -0.1330780 -0.1569648
#> [4,] 0.1874867 0.1686008
#> [5,] 0.6083038 0.6416611
predict(fit1, type = "coef")
#> 21 x 68 sparse Matrix of class "dgCMatrix"
#> [[ suppressing 68 column names ‘s0’, ‘s1’, ‘s2’ ... ]]
#>
#> (Intercept) 0.1316156 0.1279638 0.1246363 0.1206031585 0.11466554
#> V1 . . . . .
#> V2 . . . -0.0089984551 -0.02502290
#> V3 . . . . .
#> V4 . . . . .
#> V5 . . . . .
#> V6 . . . . .
#> V7 . . . -0.0003756067 -0.01171576
#> V8 . . . . .
#> V9 . . . . .
#> V10 . . . . .
#> V11 . . . . .
#> V12 . . . . .
#> V13 . . . . .
#> V14 . . . . .
#> V15 . . . . .
#> V16 . . . . .
#> V17 . . . . .
#> V18 . . . . .
#> V19 . . . . .
#> V20 . -0.0213063 -0.0407198 -0.0588843499 -0.07381744
#>
#> (Intercept) 0.10925529 0.104633842 0.10151451 0.09906752 0.0979350382
#> V1 . . . . .
#> V2 -0.03962329 -0.053002965 -0.06545831 -0.07838357 -0.0890201175
#> V3 . . . . .
#> V4 . . . . .
#> V5 . . . . .
#> V6 . . . . .
#> V7 -0.02204972 -0.031534360 -0.04043706 -0.05103997 -0.0611521832
#> V8 . . . . .
#> V9 . . . . -0.0006521341
#> V10 . . . . .
#> V11 . . . . .
#> V12 . . . . .
#> V13 . . . . .
#> V14 . . . . 0.0112544966
#> V15 . -0.002420237 -0.01321007 -0.02303216 -0.0315593813
#> V16 . . . . .
#> V17 . . . 0.01560193 0.0323546994
#> V18 . . . . .
#> V19 . . . . 0.0024703988
#> V20 -0.08742365 -0.099317313 -0.10836374 -0.11599506 -0.1235406551
#>
#> (Intercept) 0.096932918 0.094977334 0.09279798 0.090812535 0.089108757
#> V1 . . . . .
#> V2 -0.097905546 -0.105886408 -0.11311567 -0.119704452 -0.125253075
#> V3 . . . . .
#> V4 . . . . .
#> V5 . . . . .
#> V6 . . . . .
#> V7 -0.069959219 -0.078698386 -0.08693820 -0.094449269 -0.101202850
#> V8 . . . . .
#> V9 -0.007497434 -0.013782948 -0.01953398 -0.024773604 -0.029888266
#> V10 . . . . .
#> V11 . . . . .
#> V12 . -0.008908048 -0.02041643 -0.030899220 -0.040163622
#> V13 . . . . -0.002023974
#> V14 0.022580211 0.033618528 0.04395199 0.053367197 0.061993716
#> V15 -0.040130708 -0.049936972 -0.05963450 -0.068473489 -0.076320121
#> V16 . . . . .
#> V17 0.047188173 0.060567804 0.07270930 0.083773866 0.094031818
#> V18 . . . . .
#> V19 0.004909944 0.006018993 0.00660307 0.007134907 0.007493543
#> V20 -0.130066968 -0.136458110 -0.14244941 -0.147907023 -0.152896892
#>
#> (Intercept) 0.088830733 0.088916549 0.088702302 0.088509793 0.088334372
#> V1 0.003850723 0.007558762 0.010465996 0.013138978 0.015574595
#> V2 -0.129953670 -0.134628677 -0.139042672 -0.143075149 -0.146749451
#> V3 . -0.003682415 -0.009267935 -0.014339642 -0.018960750
#> V4 -0.003144036 -0.007661254 -0.011362700 -0.014748370 -0.017833287
#> V5 . . . . .
#> V6 . . . . .
#> V7 -0.107780351 -0.115092780 -0.123387643 -0.130984857 -0.137907396
#> V8 0.002494013 0.007407174 0.011612641 0.015447459 0.018941591
#> V9 -0.034169352 -0.037650430 -0.041364678 -0.044759225 -0.047852299
#> V10 . . . . .
#> V11 . . . . .
#> V12 -0.048263784 -0.057655805 -0.068759396 -0.078898838 -0.088137731
#> V13 -0.006290682 -0.010813011 -0.015692872 -0.020141154 -0.024194283
#> V14 0.068789579 0.075307812 0.081957018 0.088007935 0.093521310
#> V15 -0.083676053 -0.092059230 -0.101830448 -0.110780164 -0.118935081
#> V16 . -0.004975382 -0.015982061 -0.026039619 -0.035203890
#> V17 0.103865400 0.113869858 0.123968086 0.133189014 0.141590888
#> V18 . . . . .
#> V19 0.008141125 0.008088543 0.006387851 0.004819916 0.003391139
#> V20 -0.156550808 -0.159545770 -0.161913359 -0.164051416 -0.165999440
#>
#> (Intercept) 0.08817454 0.0880288979 0.08791080 0.08788218 0.08785893
#> V1 0.01779384 0.0198159311 0.02166005 0.02332964 0.02486118
#> V2 -0.15009734 -0.1531478081 -0.15591734 -0.15834175 -0.16055097
#> V3 -0.02317133 -0.0270078559 -0.03050325 -0.03371524 -0.03663258
#> V4 -0.02064415 -0.0232053012 -0.02554389 -0.02768812 -0.02964916
#> V5 . . . . .
#> V6 . . . . .
#> V7 -0.14421496 -0.1499621735 -0.15517571 -0.15967404 -0.16379331
#> V8 0.02212531 0.0250262034 0.02768560 0.03020073 0.03249854
#> V9 -0.05067059 -0.0532385181 -0.05556553 -0.05757630 -0.05941410
#> V10 . . . . .
#> V11 . . . . .
#> V12 -0.09655587 -0.1042261601 -0.11119928 -0.11735406 -0.12297265
#> V13 -0.02788734 -0.0312523223 -0.03430883 -0.03702371 -0.03949839
#> V14 0.09854489 0.1031221915 0.10728659 0.11102710 0.11443259
#> V15 -0.12636554 -0.1331358953 -0.13928647 -0.14467326 -0.14960651
#> V16 -0.04355403 -0.0511623752 -0.05807070 -0.06412399 -0.06965428
#> V17 0.14924636 0.1562217491 0.16256334 0.16819199 0.17333084
#> V18 . . . . .
#> V19 0.00208929 0.0009030934 . . .
#> V20 -0.16777441 -0.1693916891 -0.17086299 -0.17223889 -0.17348212
#>
#> (Intercept) 0.08793850 0.087639699 0.087011779 0.086444588 0.085927797
#> V1 0.02651418 0.028270286 0.029837775 0.031280700 0.032595648
#> V2 -0.16264497 -0.164744352 -0.166720691 -0.168527932 -0.170174616
#> V3 -0.03925929 -0.041658527 -0.043840960 -0.045810239 -0.047604475
#> V4 -0.03139266 -0.032742984 -0.033842736 -0.034862374 -0.035791484
#> V5 . . . . .
#> V6 . 0.001662191 0.004520373 0.007125755 0.009499778
#> V7 -0.16749648 -0.170962595 -0.174185630 -0.177167702 -0.179885081
#> V8 0.03454963 0.036503003 0.038358207 0.040068650 0.041627185
#> V9 -0.06102300 -0.062784295 -0.064658488 -0.066374624 -0.067938416
#> V10 -0.00204924 -0.005751921 -0.009046799 -0.012057117 -0.014800010
#> V11 . . . . .
#> V12 -0.12835012 -0.133813913 -0.138864300 -0.143491628 -0.147708029
#> V13 -0.04173349 -0.044000303 -0.046280809 -0.048360088 -0.050254647
#> V14 0.11748265 0.120353853 0.123102979 0.125604358 0.127883447
#> V15 -0.15450662 -0.159397756 -0.163773574 -0.167812905 -0.171493730
#> V16 -0.07532202 -0.081079381 -0.086278284 -0.091050153 -0.095398253
#> V17 0.17796938 0.182077990 0.185770782 0.189161705 0.192251449
#> V18 . . . . .
#> V19 . . . . .
#> V20 -0.17496892 -0.176619432 -0.178111536 -0.179452849 -0.180674856
#>
#> (Intercept) 0.08545692 0.0850456762 0.084706580 0.084393305 0.084107853
#> V1 0.03379378 0.0348324494 0.035723799 0.036543794 0.037290984
#> V2 -0.17167501 -0.1731870534 -0.174710443 -0.176093009 -0.177352763
#> V3 -0.04923932 -0.0506929191 -0.051955245 -0.053109689 -0.054161532
#> V4 -0.03663805 -0.0374662235 -0.038312550 -0.039076020 -0.039771682
#> V5 . . . . .
#> V6 0.01166290 0.0135191291 0.015064650 0.016487416 0.017783828
#> V7 -0.18236106 -0.1847707488 -0.187071077 -0.189180461 -0.191102638
#> V8 0.04304727 0.0443242652 0.045493454 0.046556396 0.047524953
#> V9 -0.06936328 -0.0706802681 -0.071849553 -0.072928413 -0.073911515
#> V10 -0.01729923 -0.0194797334 -0.021346497 -0.023056912 -0.024615400
#> V11 . . . . .
#> V12 -0.15154986 -0.1551459288 -0.158432294 -0.161447566 -0.164195147
#> V13 -0.05198090 -0.0535075412 -0.054835452 -0.056051452 -0.057159425
#> V14 0.12996007 0.1318728379 0.133618011 0.135210603 0.136661729
#> V15 -0.17484756 -0.1782088949 -0.181464244 -0.184454207 -0.187178801
#> V16 -0.09936008 -0.1029868217 -0.106263588 -0.109264191 -0.111998369
#> V17 0.19506671 0.1977568404 0.200329196 0.202672342 0.204807413
#> V18 . -0.0009618754 -0.002577328 -0.004049885 -0.005391679
#> V19 . . . . .
#> V20 -0.18178830 -0.1827516925 -0.183590192 -0.184348751 -0.185039848
#>
#> (Intercept) 0.083847760 0.083414159 0.082990396 0.082609809 0.082263063
#> V1 0.037971797 0.038713573 0.039406689 0.040038882 0.040614834
#> V2 -0.178500604 -0.179407572 -0.180191213 -0.180919253 -0.181582637
#> V3 -0.055119931 -0.055869334 -0.056516150 -0.057109787 -0.057650808
#> V4 -0.040405544 -0.040839174 -0.041203223 -0.041546410 -0.041859094
#> V5 . . . . .
#> V6 0.018965070 0.020074627 0.021123679 0.022067239 0.022926905
#> V7 -0.192854055 -0.194727081 -0.196486783 -0.198090401 -0.199551272
#> V8 0.048407466 0.049392405 0.050319967 0.051163005 0.051931050
#> V9 -0.074807281 -0.075934123 -0.077040055 -0.078030798 -0.078933356
#> V10 -0.026035437 -0.027300149 -0.028466720 -0.029521784 -0.030483104
#> V11 . -0.001714213 -0.003448373 -0.005016163 -0.006444438
#> V12 -0.166698641 -0.169317508 -0.171789208 -0.174025819 -0.176063476
#> V13 -0.058168969 -0.059199330 -0.060156001 -0.061023778 -0.061814443
#> V14 0.137983942 0.139326195 0.140567560 0.141695921 0.142724011
#> V15 -0.189661352 -0.192320289 -0.194839985 -0.197125059 -0.199206742
#> V16 -0.114489651 -0.116851504 -0.119044293 -0.121036174 -0.122850909
#> V17 0.206752811 0.208712803 0.210524804 0.212178540 0.213685212
#> V18 -0.006614272 -0.007924503 -0.009140178 -0.010249655 -0.011260469
#> V19 . . . . .
#> V20 -0.185669549 -0.186146069 -0.186558803 -0.186934604 -0.187277139
#>
#> (Intercept) 0.081947121 0.081500343 0.081029258 0.080597937 0.080204836
#> V1 0.041139617 0.041608605 0.042046761 0.042448533 0.042814743
#> V2 -0.182187087 -0.182868020 -0.183549821 -0.184173406 -0.184741708
#> V3 -0.058143769 -0.058567333 -0.058926097 -0.059249438 -0.059543868
#> V4 -0.042143998 -0.042356284 -0.042535452 -0.042699275 -0.042848582
#> V5 . . . . .
#> V6 0.023710200 0.024512769 0.025292011 0.026004711 0.026654226
#> V7 -0.200882358 -0.202414416 -0.203987906 -0.205433294 -0.206750854
#> V8 0.052630862 0.053145252 0.053578324 0.053974005 0.054334591
#> V9 -0.079755730 -0.080678883 -0.081612790 -0.082469582 -0.083250544
#> V10 -0.031359024 -0.032101883 -0.032761966 -0.033362926 -0.033910467
#> V11 -0.007745824 -0.009044053 -0.010308561 -0.011468052 -0.012524894
#> V12 -0.177920109 -0.179866699 -0.181788631 -0.183549530 -0.185154460
#> V13 -0.062534869 -0.063305175 -0.064055430 -0.064740575 -0.065364927
#> V14 0.143660768 0.144607077 0.145513470 0.146341083 0.147095251
#> V15 -0.201103485 -0.203095069 -0.205077162 -0.206896551 -0.208554972
#> V16 -0.124504425 -0.126288399 -0.128058004 -0.129678567 -0.131155562
#> V17 0.215058032 0.216500590 0.217918385 0.219216753 0.220400103
#> V18 -0.012181483 -0.013103149 -0.013993744 -0.014809097 -0.015552208
#> V19 . -0.001281906 -0.002859927 -0.004304578 -0.005621223
#> V20 -0.187589248 -0.187840604 -0.188033087 -0.188204361 -0.188360211
#>
#> (Intercept) 0.079846652 0.079536397 0.079239005 0.078966753 0.07871857
#> V1 0.043148426 0.043438600 0.043715144 0.043968670 0.04419983
#> V2 -0.185259530 -0.185717278 -0.186146972 -0.186539814 -0.18689788
#> V3 -0.059812132 -0.060078257 -0.060301492 -0.060502690 -0.06068580
#> V4 -0.042984627 -0.043108797 -0.043221401 -0.043324288 -0.04341807
#> V5 . . . . .
#> V6 0.027246047 0.027765358 0.028256614 0.028705909 0.02911545
#> V7 -0.207951395 -0.208965995 -0.209961915 -0.210876450 -0.21171041
#> V8 0.054663147 0.054955970 0.055228602 0.055477665 0.05570467
#> V9 -0.083962142 -0.084568269 -0.085158775 -0.085700471 -0.08619439
#> V10 -0.034409364 -0.034863008 -0.035277564 -0.035655045 -0.03599896
#> V11 -0.013487867 -0.014314541 -0.015113587 -0.015846120 -0.01651400
#> V12 -0.186616835 -0.187878476 -0.189092304 -0.190204239 -0.19121795
#> V13 -0.065933818 -0.066439513 -0.066911862 -0.067343228 -0.06773636
#> V14 0.147782424 0.148393985 0.148964641 0.149485640 0.14996045
#> V15 -0.210066095 -0.211351620 -0.212605231 -0.213755679 -0.21480471
#> V16 -0.132501363 -0.133668752 -0.134785762 -0.135808547 -0.13674094
#> V17 0.221478344 0.222416955 0.223311663 0.224130833 0.22487761
#> V18 -0.016229313 -0.016820600 -0.017382442 -0.017896707 -0.01836551
#> V19 -0.006820917 -0.007866234 -0.008861904 -0.009773273 -0.01060407
#> V20 -0.188502206 -0.188657473 -0.188775835 -0.188881174 -0.18897691
#>
#> (Intercept) 0.07849242 0.07830809 0.07812203 0.07794951 0.07779180
#> V1 0.04441046 0.04458936 0.04476164 0.04492162 0.04506800
#> V2 -0.18722416 -0.18750773 -0.18777692 -0.18802456 -0.18825064
#> V3 -0.06085262 -0.06102572 -0.06116746 -0.06129250 -0.06140561
#> V4 -0.04350352 -0.04358771 -0.04365823 -0.04372231 -0.04378072
#> V5 . . . . .
#> V6 0.02948862 0.02980334 0.03011073 0.03039464 0.03065402
#> V7 -0.21247036 -0.21307131 -0.21369250 -0.21427306 -0.21480475
#> V8 0.05591151 0.05609205 0.05626300 0.05641996 0.05656320
#> V9 -0.08664446 -0.08700112 -0.08736966 -0.08771352 -0.08802832
#> V10 -0.03631232 -0.03658802 -0.03684878 -0.03708667 -0.03730341
#> V11 -0.01712259 -0.01761429 -0.01811342 -0.01857779 -0.01900265
#> V12 -0.19214166 -0.19289010 -0.19364897 -0.19435381 -0.19499842
#> V13 -0.06809458 -0.06840435 -0.06870049 -0.06897258 -0.06922089
#> V14 0.15039308 0.15076666 0.15112474 0.15145346 0.15175337
#> V15 -0.21576061 -0.21652288 -0.21730496 -0.21803484 -0.21870308
#> V16 -0.13759055 -0.13829138 -0.13899003 -0.13963745 -0.14022931
#> V17 0.22555808 0.22612874 0.22668842 0.22720623 0.22767950
#> V18 -0.01879269 -0.01915276 -0.01950422 -0.01982916 -0.02012612
#> V19 -0.01136110 -0.01199322 -0.01261610 -0.01319242 -0.01371916
#> V20 -0.18906412 -0.18917028 -0.18924638 -0.18931081 -0.18936857
#>
#> (Intercept) 0.07768047 0.07752221 0.07742630 0.07732282 0.07722326
#> V1 0.04518615 0.04531875 0.04541961 0.04551720 0.04560887
#> V2 -0.18844557 -0.18864103 -0.18880536 -0.18895949 -0.18910156
#> V3 -0.06151669 -0.06160785 -0.06169662 -0.06177800 -0.06184972
#> V4 -0.04385128 -0.04388378 -0.04394148 -0.04398531 -0.04402174
#> V5 . . . . .
#> V6 0.03084872 0.03109953 0.03126518 0.03143774 0.03160129
#> V7 -0.21518052 -0.21570858 -0.21603597 -0.21638440 -0.21671962
#> V8 0.05668399 0.05681114 0.05691248 0.05701113 0.05710164
#> V9 -0.08824667 -0.08856370 -0.08875367 -0.08895823 -0.08915653
#> V10 -0.03746572 -0.03767948 -0.03781515 -0.03796214 -0.03810004
#> V11 -0.01930770 -0.01972755 -0.01999117 -0.02027092 -0.02053895
#> V12 -0.19545451 -0.19609918 -0.19649304 -0.19691632 -0.19732340
#> V13 -0.06941815 -0.06964962 -0.06981583 -0.06998363 -0.07014039
#> V14 0.15199185 0.15227133 0.15247241 0.15267519 0.15286464
#> V15 -0.21918148 -0.21984036 -0.22025589 -0.22069331 -0.22111428
#> V16 -0.14067272 -0.14124293 -0.14162294 -0.14201573 -0.14238905
#> V17 0.22805824 0.22849210 0.22881463 0.22913238 0.22943027
#> V18 -0.02036518 -0.02063623 -0.02083966 -0.02103886 -0.02122566
#> V19 -0.01412609 -0.01462275 -0.01497010 -0.01532124 -0.01565306
#> V20 -0.18944523 -0.18947617 -0.18953497 -0.18958027 -0.18961683
#>
#> (Intercept) 0.07713080 0.07704598 0.07696851 0.07689786 0.07683347
#> V1 0.04569362 0.04577131 0.04584226 0.04590696 0.04596593
#> V2 -0.18923170 -0.18935051 -0.18945886 -0.18955761 -0.18964759
#> V3 -0.06191389 -0.06197189 -0.06202456 -0.06207248 -0.06211612
#> V4 -0.04405394 -0.04408302 -0.04410943 -0.04413347 -0.04415537
#> V5 . . . . .
#> V6 0.03175248 0.03189100 0.03201747 0.03213279 0.03223790
#> V7 -0.21703130 -0.21731744 -0.21757889 -0.21781737 -0.21803475
#> V8 0.05718427 0.05725962 0.05732831 0.05739090 0.05744794
#> V9 -0.08934133 -0.08951113 -0.08966631 -0.08980787 -0.08993691
#> V10 -0.03822649 -0.03834190 -0.03844710 -0.03854297 -0.03863033
#> V11 -0.02078766 -0.02101581 -0.02122421 -0.02141428 -0.02158751
#> V12 -0.19770130 -0.19804792 -0.19836450 -0.19865321 -0.19891635
#> V13 -0.07028443 -0.07041608 -0.07053617 -0.07064563 -0.07074539
#> V14 0.15303863 0.15319760 0.15334259 0.15347475 0.15359518
#> V15 -0.22150564 -0.22186490 -0.22219314 -0.22249253 -0.22276543
#> V16 -0.14273431 -0.14305062 -0.14333941 -0.14360273 -0.14384273
#> V17 0.22970468 0.22995577 0.23018492 0.23039384 0.23058424
#> V18 -0.02139776 -0.02155523 -0.02169892 -0.02182993 -0.02194933
#> V19 -0.01595947 -0.01624003 -0.01649615 -0.01672966 -0.01694249
#> V20 -0.18964825 -0.18967619 -0.18970141 -0.18972430 -0.18974513
#>
#> (Intercept) 0.07677480 0.07672133 0.07667261
#> V1 0.04601967 0.04606863 0.04611325
#> V2 -0.18972959 -0.18980430 -0.18987238
#> V3 -0.06215588 -0.06219210 -0.06222510
#> V4 -0.04417533 -0.04419351 -0.04421008
#> V5 . . .
#> V6 0.03233368 0.03242095 0.03250047
#> V7 -0.21823285 -0.21841336 -0.21857783
#> V8 0.05749991 0.05754727 0.05759042
#> V9 -0.09005450 -0.09016165 -0.09025928
#> V10 -0.03870992 -0.03878245 -0.03884853
#> V11 -0.02174538 -0.02188923 -0.02202030
#> V12 -0.19915615 -0.19937465 -0.19957374
#> V13 -0.07083629 -0.07091912 -0.07099459
#> V14 0.15370491 0.15380490 0.15389601
#> V15 -0.22301412 -0.22324073 -0.22344721
#> V16 -0.14406143 -0.14426070 -0.14444228
#> V17 0.23075774 0.23091584 0.23105989
#> V18 -0.02205813 -0.02215726 -0.02224759
#> V19 -0.01713642 -0.01731314 -0.01747415
#> V20 -0.18976409 -0.18978137 -0.18979712
plot(fit1, xvar = "lambda")
fit2 = glmnet(x, g2, family = "binomial")
predict(fit2, type = "response", newx = x[2:5, ])
#> s0 s1 s2 s3 s4 s5 s6 s7
#> [1,] 0.5 0.4957157 0.4908455 0.4863793 0.4815442 0.4767801 0.4666765 0.4574560
#> [2,] 0.5 0.5025976 0.5058101 0.5087605 0.5163690 0.5248731 0.5324840 0.5394615
#> [3,] 0.5 0.4987810 0.4966490 0.4946910 0.4936164 0.4927998 0.4891055 0.4858994
#> [4,] 0.5 0.4984396 0.5012374 0.5038222 0.5081674 0.5127468 0.5145375 0.5160468
#> s8 s9 s10 s11 s12 s13 s14
#> [1,] 0.4500921 0.4442138 0.4370733 0.4304967 0.4244371 0.4190290 0.4154664
#> [2,] 0.5454355 0.5500309 0.5517282 0.5533449 0.5548842 0.5564669 0.5589569
#> [3,] 0.4873589 0.4926685 0.5054378 0.5171682 0.5279357 0.5379818 0.5485419
#> [4,] 0.5136739 0.5118174 0.5078679 0.5042446 0.5009194 0.4973195 0.4895555
#> s15 s16 s17 s18 s19 s20 s21
#> [1,] 0.4121643 0.4091068 0.4062638 0.4026114 0.3992400 0.3934562 0.3859047
#> [2,] 0.5613070 0.5635178 0.5655842 0.5666097 0.5675869 0.5688657 0.5653795
#> [3,] 0.5582203 0.5670853 0.5752672 0.5876416 0.5989202 0.6110131 0.6196884
#> [4,] 0.4824223 0.4758711 0.4698606 0.4645972 0.4597727 0.4544830 0.4486175
#> s22 s23 s24 s25 s26 s27 s28
#> [1,] 0.3784227 0.3715556 0.3652568 0.3589393 0.3526053 0.3467934 0.3414857
#> [2,] 0.5612872 0.5575643 0.5541776 0.5519367 0.5507556 0.5492340 0.5478493
#> [3,] 0.6265977 0.6329107 0.6386762 0.6439121 0.6486577 0.6526689 0.6563274
#> [4,] 0.4429672 0.4377808 0.4330225 0.4282271 0.4233807 0.4181931 0.4134501
#> s29 s30 s31 s32 s33 s34 s35
#> [1,] 0.3366392 0.3322146 0.3284584 0.3255266 0.3228508 0.3203979 0.3182436
#> [2,] 0.5465888 0.5454412 0.5437434 0.5399442 0.5365221 0.5333799 0.5306994
#> [3,] 0.6596646 0.6627088 0.6651596 0.6645474 0.6641173 0.6637096 0.6631769
#> [4,] 0.4091154 0.4051546 0.4012907 0.3975394 0.3940882 0.3909464 0.3883306
#> s36 s37 s38 s39 s40 s41 s42
#> [1,] 0.3162980 0.3145767 0.3130047 0.3115693 0.3102686 0.3090721 0.3079796
#> [2,] 0.5282865 0.5259661 0.5238441 0.5219049 0.5201509 0.5185318 0.5170526
#> [3,] 0.6626686 0.6625323 0.6624049 0.6622870 0.6621922 0.6620911 0.6619974
#> [4,] 0.3860114 0.3841210 0.3823934 0.3808149 0.3793661 0.3780496 0.3768476
#> s43 s44 s45 s46 s47 s48 s49
#> [1,] 0.3069827 0.3060730 0.3052550 0.3044977 0.3038062 0.3031754 0.3026000
#> [2,] 0.5157018 0.5144686 0.5133644 0.5123367 0.5113976 0.5105406 0.5097587
#> [3,] 0.6619111 0.6618317 0.6617761 0.6617088 0.6616459 0.6615881 0.6615352
#> [4,] 0.3757502 0.3747485 0.3738270 0.3729927 0.3722320 0.3715380 0.3709049
#> s50 s51 s52 s53 s54 s55
#> [1,] 0.3020893 0.3016113 0.3011740 0.3008085 0.3004892 0.3003234
#> [2,] 0.5090687 0.5084188 0.5078237 0.5071890 0.5065353 0.5062173
#> [3,] 0.6615083 0.6614644 0.6614221 0.6613236 0.6611511 0.6612511
#> [4,] 0.3703220 0.3697946 0.3693146 0.3690231 0.3688828 0.3687720
predict(fit2, type = "nonzero")
#> $s0
#> NULL
#>
#> $s1
#> [1] 9 10 15
#>
#> $s2
#> [1] 9 10 15
#>
#> $s3
#> [1] 9 10 15
#>
#> $s4
#> [1] 6 9 10 15
#>
#> $s5
#> [1] 5 6 9 10 15
#>
#> $s6
#> [1] 5 6 9 10 15
#>
#> $s7
#> [1] 2 5 6 9 10 15
#>
#> $s8
#> [1] 2 5 6 9 10 15
#>
#> $s9
#> [1] 1 2 5 6 9 10 15 18
#>
#> $s10
#> [1] 1 2 5 6 9 10 15 18
#>
#> $s11
#> [1] 1 2 5 6 9 10 15 18
#>
#> $s12
#> [1] 1 2 5 6 9 10 15 18
#>
#> $s13
#> [1] 1 2 5 6 9 10 15 18 19
#>
#> $s14
#> [1] 1 2 5 6 9 10 15 18 19
#>
#> $s15
#> [1] 1 2 5 6 9 10 15 18 19
#>
#> $s16
#> [1] 1 2 5 6 9 10 15 18 19
#>
#> $s17
#> [1] 1 2 5 6 9 10 13 15 18 19
#>
#> $s18
#> [1] 1 2 5 6 9 10 13 15 18 19
#>
#> $s19
#> [1] 1 2 5 6 9 10 13 15 18 19
#>
#> $s20
#> [1] 1 2 4 5 6 9 10 13 15 18 19
#>
#> $s21
#> [1] 1 2 4 5 6 7 9 10 12 13 15 18 19
#>
#> $s22
#> [1] 1 2 4 5 6 7 9 10 12 13 15 18 19
#>
#> $s23
#> [1] 1 2 4 5 6 7 9 10 12 13 15 18 19
#>
#> $s24
#> [1] 1 2 4 5 6 7 9 10 12 13 15 18 19
#>
#> $s25
#> [1] 1 2 4 5 6 7 9 10 11 12 13 15 18 19
#>
#> $s26
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 18 19
#>
#> $s27
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 18 19
#>
#> $s28
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 18 19
#>
#> $s29
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 18 19
#>
#> $s30
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 18 19
#>
#> $s31
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 16 18 19 20
#>
#> $s32
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 16 18 19 20
#>
#> $s33
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 16 18 19 20
#>
#> $s34
#> [1] 1 2 3 4 5 6 7 9 10 11 12 13 15 16 18 19 20
#>
#> $s35
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 15 16 18 19 20
#>
#> $s36
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s37
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s38
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s39
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s40
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s41
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s42
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s43
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s44
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s45
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s46
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s47
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s48
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s49
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s50
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s51
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s52
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 18 19 20
#>
#> $s53
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#>
#> $s54
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#>
#> $s55
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
#>
fit3 = glmnet(x, g4, family = "multinomial")
predict(fit3, newx = x[1:3, ], type = "response", s = 0.01)
#> , , 1
#>
#> 1 2 3 4
#> [1,] 0.3528253 0.3347243 0.27440451 0.03804590
#> [2,] 0.0979950 0.7873472 0.07355998 0.04109778
#> [3,] 0.4251785 0.4073988 0.04693317 0.12048947
#>