gic.ncpen: gic.ncpen: compute the generalized information criterion...
In ncpen: Unified Algorithm for Non-convex Penalized Estimation for Generalized Linear Models

Description Usage Arguments Details Value Author(s) References See Also Examples

The function provides the selection of the regularization parameter lambda based on the GIC including AIC and BIC.

1	gic.ncpen(fit, weight = NULL, verbose = TRUE, ...)

`fit`	(ncpen object) fitted `ncpen` object.
`weight`	(numeric) the weight factor for various information criteria. Default is BIC if `n>p` and GIC if `n<p` (see details).
`verbose`	(logical) whether to plot the GIC curve.
`...`	other graphical parameters to `plot`.

User can supply various weight values (see references). For example, weight=2, weight=log(n), weight=log(log(p))log(n), weight=log(log(n))log(p), corresponds to AIC, BIC (fixed dimensional model), modified BIC (diverging dimensional model) and GIC (high dimensional model).

The coefficients matrix.

`gic`	the GIC values.
`lambda`	the sequence of lambda values used to calculate GIC.
`opt.beta`	the optimal coefficients selected by GIC.
`opt.lambda`	the optimal lambda value.

Dongshin Kim, Sunghoon Kwon, Sangin Lee

Wang, H., Li, R. and Tsai, C.L. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika, 94(3), 553-568. Wang, H., Li, B. and Leng, C. (2009). Shrinkage tuning parameter selection with a diverging number of parameters. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(3), 671-683. Kim, Y., Kwon, S. and Choi, H. (2012). Consistent Model Selection Criteria on High Dimensions. Journal of Machine Learning Research, 13, 1037-1057. Fan, Y. and Tang, C.Y. (2013). Tuning parameter selection in high dimensional penalized likelihood. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 75(3), 531-552. Lee, S., Kwon, S. and Kim, Y. (2016). A modified local quadratic approximation algorithm for penalized optimization problems. Computational Statistics and Data Analysis, 94, 275-286.

ncpen

### linear regression with scad penalty
sam =  sam.gen.ncpen(n=200,p=20,q=5,cf.min=0.5,cf.max=1,corr=0.5)
x.mat = sam$x.mat; y.vec = sam$y.vec
fit = ncpen(y.vec=y.vec,x.mat=x.mat)
gic.ncpen(fit,pch="*",type="b")
### multinomial regression with classo penalty
sam =  sam.gen.ncpen(n=200,p=20,q=5,k=3,cf.min=0.5,cf.max=1,corr=0.5,family="multinomial")
x.mat = sam$x.mat; y.vec = sam$y.vec
fit = ncpen(y.vec=y.vec,x.mat=x.mat,family="multinomial",penalty="classo")
gic.ncpen(fit,pch="*",type="b")

$gic
  [1] 423.7131 423.7131 418.8934 404.4903 391.7829 380.5626 370.6469 361.8766
  [9] 354.1122 347.2320 341.1294 335.7110 327.0331 318.3402 311.0836 305.0588
 [17] 300.0863 300.7567 291.6703 279.2499 274.4702 281.1054 267.6913 250.3692
 [25] 231.6707 220.5904 200.9133 196.6216 196.0883 195.6429 205.4020 204.5306
 [33] 203.7699 203.1055 202.3547 201.7137 201.1789 211.2348 210.6936 210.2471
 [41] 209.8689 209.5100 214.2556 213.9065 213.6196 218.6705 218.4366 223.4167
 [49] 228.2994 227.9980 226.7421 226.7282 232.0183 232.0008 237.2324 237.1238
 [57] 237.0276 242.1892 242.0149 247.0367 246.9431 246.8322 246.6012 246.5916
 [65] 246.5836 246.5796 246.5787 246.5787 246.5787 246.5787 246.5787 246.5787
 [73] 246.5787 246.5787 246.5787 246.5787 246.5787 246.5787 251.8765 257.1733
 [81] 257.1722 257.1713 257.1705 257.1699 257.1683 257.1670 257.1673 257.1676
 [89] 257.1676 257.1676 257.1676 257.1676 257.1676 257.1676 257.1676 257.1676
 [97] 257.1676 257.1676 257.1676 257.1676

$lambda
  [1] 0.9395993318 0.8762734815 0.8172155817 0.7621379866 0.7107724371
  [6] 0.6628687537 0.6181936182 0.5765294374 0.5376732829 0.5014359031
 [11] 0.4676408015 0.4361233766 0.4067301207 0.3793178718 0.3537531168
 [16] 0.3299113407 0.3076764205 0.2869400595 0.2676012599 0.2495658306
 [21] 0.2327459289 0.2170596322 0.2024305395 0.1887873987 0.1760637598
 [26] 0.1641976517 0.1531312795 0.1428107438 0.1331857776 0.1242095020
 [31] 0.1158381973 0.1080310905 0.1007501565 0.0939599332 0.0876273482
 [36] 0.0817215582 0.0762137987 0.0710772437 0.0662868754 0.0618193618
 [41] 0.0576529437 0.0537673283 0.0501435903 0.0467640802 0.0436123377
 [46] 0.0406730121 0.0379317872 0.0353753117 0.0329911341 0.0307676421
 [51] 0.0286940060 0.0267601260 0.0249565831 0.0232745929 0.0217059632
 [56] 0.0202430540 0.0188787399 0.0176063760 0.0164197652 0.0153131280
 [61] 0.0142810744 0.0133185778 0.0124209502 0.0115838197 0.0108031090
 [66] 0.0100750157 0.0093959933 0.0087627348 0.0081721558 0.0076213799
 [71] 0.0071077244 0.0066286875 0.0061819362 0.0057652944 0.0053767328
 [76] 0.0050143590 0.0046764080 0.0043612338 0.0040673012 0.0037931787
 [81] 0.0035375312 0.0032991134 0.0030767642 0.0028694006 0.0026760126
 [86] 0.0024956583 0.0023274593 0.0021705963 0.0020243054 0.0018878740
 [91] 0.0017606376 0.0016419765 0.0015313128 0.0014281074 0.0013318578
 [96] 0.0012420950 0.0011583820 0.0010803109 0.0010075016 0.0009395993

$opt.lambda
[1] 0.1242095

$opt.beta
  intercept          x1          x2          x3          x4          x5 
 0.03904388 -0.90624053  0.72448899 -0.60804090  0.53945700 -0.51361994 
         x6          x7          x8          x9         x10         x11 
 0.00000000  0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 
        x12         x13         x14         x15         x16         x17 
 0.00000000  0.00000000  0.00000000  0.00000000  0.00000000 -0.06476728 
        x18         x19         x20 
 0.00000000  0.00000000  0.00000000 

$gic
  [1] 439.1201 439.1201 439.1201 413.3054 413.3054 413.3054 413.3054 413.3054
  [9] 413.3054 399.1233 399.1233 399.1233 399.1233 385.3695 385.3695 362.5073
 [17] 362.5073 362.5073 362.5073 362.5073 348.3072 348.3072 348.3072 348.3072
 [25] 348.3072 348.3072 348.3072 348.3072 349.0423 349.0423 349.0423 349.0423
 [33] 349.0423 349.0423 357.8026 357.8026 357.8026 357.8026 361.4760 361.4760
 [41] 367.3735 367.3735 367.3735 370.5104 374.4214 374.4214 389.0989 389.0989
 [49] 389.0989 389.0989 389.0989 402.5196 411.6900 416.2593 421.0574 421.0574
 [57] 421.0574 421.0574 429.0568 429.0568 429.0568 429.0568 429.0568 429.0568
 [65] 429.0568 429.0568 429.0568 429.0568 439.1463 439.1463 439.1463 444.2339
 [73] 444.2339 444.2339 444.2339 444.2339 444.2339 444.2339 454.5880 454.5880
 [81] 454.5880 454.5880 454.5880 454.5880 459.8262 459.8262 459.8262 459.8262
 [89] 465.0843 465.0843 465.0843 470.3805 470.3805 470.3805 470.3805 470.3805
 [97] 470.3805 475.6751 475.6751 475.6751

$lambda
  [1] 0.195038755 0.186173943 0.177712050 0.169634763 0.161924601 0.154564878
  [7] 0.147539666 0.140833760 0.134432649 0.128322477 0.122490023 0.116922662
 [13] 0.111608347 0.106535575 0.101693369 0.097071248 0.092659210 0.088447706
 [19] 0.084427621 0.080590256 0.076927304 0.073430839 0.070093294 0.066907446
 [25] 0.063866399 0.060963573 0.058192684 0.055547737 0.053023007 0.050613029
 [31] 0.048312589 0.046116707 0.044020632 0.042019826 0.040109960 0.038286901
 [37] 0.036546702 0.034885598 0.033299994 0.031786457 0.030341714 0.028962636
 [43] 0.027646240 0.026389675 0.025190224 0.024045289 0.022952394 0.021909172
 [49] 0.020913366 0.019962822 0.019055481 0.018189380 0.017362644 0.016573485
 [55] 0.015820195 0.015101143 0.014414772 0.013759599 0.013134204 0.012537234
 [61] 0.011967397 0.011423461 0.010904247 0.010408632 0.009935543 0.009483958
 [67] 0.009052897 0.008641429 0.008248663 0.007873748 0.007515874 0.007174266
 [73] 0.006848185 0.006536924 0.006239811 0.005956202 0.005685483 0.005427069
 [79] 0.005180401 0.004944943 0.004720188 0.004505648 0.004300860 0.004105379
 [85] 0.003918783 0.003740668 0.003570649 0.003408358 0.003253443 0.003105569
 [91] 0.002964416 0.002829678 0.002701065 0.002578298 0.002461110 0.002349249
 [97] 0.002242472 0.002140548 0.002043257 0.001950388

$opt.lambda
[1] 0.0769273

$opt.beta
          class1      class2 class3
 [1,] -0.1792295 -0.07667944      0
 [2,]  1.3909870  1.14765763      0
 [3,]  0.0000000  0.00000000      0
 [4,]  0.0000000  0.61681522      0
 [5,]  1.2761182  1.63523645      0
 [6,]  0.4424590  0.00000000      0
 [7,]  0.0000000  0.00000000      0
 [8,]  0.0000000  0.00000000      0
 [9,]  0.0000000  0.00000000      0
[10,]  0.0000000  0.00000000      0
[11,]  0.0000000  0.00000000      0
[12,]  0.0000000  0.00000000      0
[13,]  0.0000000  0.00000000      0
[14,]  0.0000000  0.00000000      0
[15,]  0.0000000  0.00000000      0
[16,]  0.0000000  0.00000000      0
[17,]  0.0000000  0.00000000      0
[18,]  0.0000000  0.00000000      0
[19,]  0.0000000  0.00000000      0
[20,]  0.0000000  0.00000000      0
[21,]  0.0000000  0.00000000      0