infocr: Model Selection Criteria for Ridge Regression

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

Description

The infocr.lmridge function computes model information selection criteria (AIC and BIC), see Akaike, 1974 <https://doi.org/10.1109/TAC.1974.1100705>; Imdad, 2017 and Schwarz, 1978 <https://doi.org/10.1214/aos/1176344136>).

Usage

1
2
3
infocr(object, ...)
## S3 method for class 'lmridge'
infocr(object, ...)

Arguments

object

An object of class "lmridge".

...

Not presently used in this implementation.

Details

Model information selection criteria are common way of selecting among model while balancing the competing goals of fit and parsimony. The model selection criteria AIC and BIC are computed by quantifying df in the ridge regression model, using formula (trace[X(X'X+kI)^{-1}X']). It can be helpful for selecting optimal value of biasing parameter K.

Value

It returns a matrix of information criteria, AIC and BIC for each biasing parameter K. Column of matrix indicates model selection criteria AIC and BIC, respectively, while rows indicate value of biasing parameter K for which model selection criteria are computed.

Author(s)

Muhammad Imdad Ullah, Muhammad Aslam

References

Akaike, H. (1974). A new look at the Statistical Model Identification. IEEE Transaction on Automatic Control, 9(6), 716-723. Akaike, 1974.

Imdad, M. U. Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan), 2017.

Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461–464. Schwarz, 1978.

See Also

the ridge model fitting lmridge, ridge AIC and BIC plot info.plot

Examples

1
2
3
4
5
6
7
8
mod <- lmridge(y~., as.data.frame(Hald), K = seq(0, .2, 0.001))
infocr(mod)

## Vector of AIC values
infocr(mod)[,1]

## vector of BIC values
infocr(mod)[,2]

Example output

             AIC      BIC
K=0     24.94429 60.54843
K=0.001 24.19586 59.58105
K=0.002 23.87176 59.15690
K=0.003 23.68864 58.91546
K=0.004 23.56981 58.75782
K=0.005 23.48594 58.64582
K=0.006 23.42344 58.56170
K=0.007 23.37495 58.49582
K=0.008 23.33638 58.44281
K=0.009 23.30510 58.39917
K=0.01  23.27944 58.36274
K=0.011 23.25820 58.33192
K=0.012 23.24068 58.30578
K=0.013 23.22616 58.28339
K=0.014 23.21426 58.26424
K=0.015 23.20463 58.24788
K=0.016 23.19693 58.23386
K=0.017 23.19107 58.22206
K=0.018 23.18679 58.21214
K=0.019 23.18394 58.20391
K=0.02  23.18250 58.19735
K=0.021 23.18219 58.19209
K=0.022 23.18313 58.18829
K=0.023 23.18511 58.18568
K=0.024 23.18815 58.18430
K=0.025 23.19211 58.18394
K=0.026 23.19699 58.18463
K=0.027 23.20276 58.18634
K=0.028 23.20936 58.18897
K=0.029 23.21667 58.19238
K=0.03  23.22477 58.19668
K=0.031 23.23365 58.20185
K=0.032 23.24322 58.20779
K=0.033 23.25342 58.21442
K=0.034 23.26424 58.22172
K=0.035 23.27569 58.22970
K=0.036 23.28785 58.23850
K=0.037 23.30042 58.24771
K=0.038 23.31368 58.25769
K=0.039 23.32749 58.26827
K=0.04  23.34170 58.27927
K=0.041 23.35659 58.29103
K=0.042 23.37190 58.30325
K=0.043 23.38763 58.31590
K=0.044 23.40392 58.32917
K=0.045 23.42062 58.34289
K=0.046 23.43781 58.35713
K=0.047 23.45540 58.37180
K=0.048 23.47339 58.38690
K=0.049 23.49179 58.40245
K=0.05  23.51058 58.41842
K=0.051 23.52978 58.43484
K=0.052 23.54934 58.45163
K=0.053 23.56926 58.46882
K=0.054 23.58954 58.48640
K=0.055 23.61018 58.50435
K=0.056 23.63113 58.52265
K=0.057 23.65241 58.54130
K=0.058 23.67402 58.56030
K=0.059 23.69594 58.57963
K=0.06  23.71811 58.59924
K=0.061 23.74067 58.61927
K=0.062 23.76345 58.63953
K=0.063 23.78657 58.66018
K=0.064 23.80992 58.68105
K=0.065 23.83352 58.70219
K=0.066 23.85738 58.72362
K=0.067 23.88151 58.74534
K=0.068 23.90594 58.76739
K=0.069 23.93053 58.78959
K=0.07  23.95538 58.81208
K=0.071 23.98047 58.83485
K=0.072 24.00575 58.85779
K=0.073 24.03128 58.88103
K=0.074 24.05703 58.90449
K=0.075 24.08298 58.92817
K=0.076 24.10913 58.95208
K=0.077 24.13544 58.97615
K=0.078 24.16199 59.00048
K=0.079 24.18867 59.02494
K=0.08  24.21557 59.04966
K=0.081 24.24268 59.07461
K=0.082 24.26991 59.09968
K=0.083 24.29734 59.12496
K=0.084 24.32494 59.15044
K=0.085 24.35263 59.17600
K=0.086 24.38055 59.20182
K=0.087 24.40863 59.22782
K=0.088 24.43681 59.25393
K=0.089 24.46515 59.28020
K=0.09  24.49360 59.30660
K=0.091 24.52225 59.33321
K=0.092 24.55096 59.35989
K=0.093 24.57988 59.38681
K=0.094 24.60892 59.41386
K=0.095 24.63802 59.44097
K=0.096 24.66728 59.46826
K=0.097 24.69662 59.49562
K=0.098 24.72614 59.52321
K=0.099 24.75574 59.55087
K=0.1   24.78545 59.57865
K=0.101 24.81528 59.60657
K=0.102 24.84513 59.63450
K=0.103 24.87518 59.66268
K=0.104 24.90530 59.69091
K=0.105 24.93543 59.71915
K=0.106 24.96583 59.74772
K=0.107 24.99619 59.77622
K=0.108 25.02666 59.80485
K=0.109 25.05721 59.83357
K=0.11  25.08784 59.86237
K=0.111 25.11860 59.89134
K=0.112 25.14937 59.92030
K=0.113 25.18028 59.94943
K=0.114 25.21119 59.97855
K=0.115 25.24220 60.00778
K=0.116 25.27332 60.03716
K=0.117 25.30444 60.06651
K=0.118 25.33565 60.09598
K=0.119 25.36693 60.12552
K=0.12  25.39830 60.15518
K=0.121 25.42968 60.18483
K=0.122 25.46114 60.21459
K=0.123 25.49263 60.24437
K=0.124 25.52425 60.27431
K=0.125 25.55584 60.30421
K=0.126 25.58752 60.33422
K=0.127 25.61929 60.36434
K=0.128 25.65105 60.39444
K=0.129 25.68286 60.42460
K=0.13  25.71468 60.45477
K=0.131 25.74660 60.48507
K=0.132 25.77856 60.51540
K=0.133 25.81052 60.54574
K=0.134 25.84256 60.57617
K=0.135 25.87459 60.60659
K=0.136 25.90670 60.63712
K=0.137 25.93884 60.66768
K=0.138 25.97097 60.69822
K=0.139 26.00315 60.72882
K=0.14  26.03543 60.75955
K=0.141 26.06763 60.79018
K=0.142 26.09997 60.82099
K=0.143 26.13228 60.85176
K=0.144 26.16459 60.88252
K=0.145 26.19695 60.91336
K=0.146 26.22930 60.94418
K=0.147 26.26168 60.97504
K=0.148 26.29412 61.00598
K=0.149 26.32658 61.03694
K=0.15  26.35903 61.06789
K=0.151 26.39150 61.09887
K=0.152 26.42400 61.12989
K=0.153 26.45651 61.16093
K=0.154 26.48906 61.19201
K=0.155 26.52161 61.22311
K=0.156 26.55414 61.25418
K=0.157 26.58674 61.28533
K=0.158 26.61929 61.31643
K=0.159 26.65191 61.34762
K=0.16  26.68447 61.37874
K=0.161 26.71708 61.40993
K=0.162 26.74974 61.44118
K=0.163 26.78230 61.47232
K=0.164 26.81495 61.50357
K=0.165 26.84757 61.53477
K=0.166 26.88019 61.56599
K=0.167 26.91287 61.59730
K=0.168 26.94550 61.62853
K=0.169 26.97817 61.65983
K=0.17  27.01084 61.69113
K=0.171 27.04347 61.72239
K=0.172 27.07611 61.75366
K=0.173 27.10880 61.78501
K=0.174 27.14143 61.81629
K=0.175 27.17409 61.84760
K=0.176 27.20674 61.87891
K=0.177 27.23939 61.91023
K=0.178 27.27200 61.94150
K=0.179 27.30463 61.97280
K=0.18  27.33725 62.00410
K=0.181 27.36989 62.03543
K=0.182 27.40253 62.06676
K=0.183 27.43510 62.09802
K=0.184 27.46771 62.12933
K=0.185 27.50035 62.16069
K=0.186 27.53291 62.19195
K=0.187 27.56548 62.22323
K=0.188 27.59809 62.25457
K=0.189 27.63063 62.28583
K=0.19  27.66320 62.31713
K=0.191 27.69571 62.34836
K=0.192 27.72829 62.37969
K=0.193 27.76082 62.41097
K=0.194 27.79328 62.44217
K=0.195 27.82576 62.47339
K=0.196 27.85830 62.50471
K=0.197 27.89074 62.53589
K=0.198 27.92321 62.56713
K=0.199 27.95568 62.59839
K=0.2   27.98813 62.62961
     K=0  K=0.001  K=0.002  K=0.003  K=0.004  K=0.005  K=0.006  K=0.007 
24.94429 24.19586 23.87176 23.68864 23.56981 23.48594 23.42344 23.37495 
 K=0.008  K=0.009   K=0.01  K=0.011  K=0.012  K=0.013  K=0.014  K=0.015 
23.33638 23.30510 23.27944 23.25820 23.24068 23.22616 23.21426 23.20463 
 K=0.016  K=0.017  K=0.018  K=0.019   K=0.02  K=0.021  K=0.022  K=0.023 
23.19693 23.19107 23.18679 23.18394 23.18250 23.18219 23.18313 23.18511 
 K=0.024  K=0.025  K=0.026  K=0.027  K=0.028  K=0.029   K=0.03  K=0.031 
23.18815 23.19211 23.19699 23.20276 23.20936 23.21667 23.22477 23.23365 
 K=0.032  K=0.033  K=0.034  K=0.035  K=0.036  K=0.037  K=0.038  K=0.039 
23.24322 23.25342 23.26424 23.27569 23.28785 23.30042 23.31368 23.32749 
  K=0.04  K=0.041  K=0.042  K=0.043  K=0.044  K=0.045  K=0.046  K=0.047 
23.34170 23.35659 23.37190 23.38763 23.40392 23.42062 23.43781 23.45540 
 K=0.048  K=0.049   K=0.05  K=0.051  K=0.052  K=0.053  K=0.054  K=0.055 
23.47339 23.49179 23.51058 23.52978 23.54934 23.56926 23.58954 23.61018 
 K=0.056  K=0.057  K=0.058  K=0.059   K=0.06  K=0.061  K=0.062  K=0.063 
23.63113 23.65241 23.67402 23.69594 23.71811 23.74067 23.76345 23.78657 
 K=0.064  K=0.065  K=0.066  K=0.067  K=0.068  K=0.069   K=0.07  K=0.071 
23.80992 23.83352 23.85738 23.88151 23.90594 23.93053 23.95538 23.98047 
 K=0.072  K=0.073  K=0.074  K=0.075  K=0.076  K=0.077  K=0.078  K=0.079 
24.00575 24.03128 24.05703 24.08298 24.10913 24.13544 24.16199 24.18867 
  K=0.08  K=0.081  K=0.082  K=0.083  K=0.084  K=0.085  K=0.086  K=0.087 
24.21557 24.24268 24.26991 24.29734 24.32494 24.35263 24.38055 24.40863 
 K=0.088  K=0.089   K=0.09  K=0.091  K=0.092  K=0.093  K=0.094  K=0.095 
24.43681 24.46515 24.49360 24.52225 24.55096 24.57988 24.60892 24.63802 
 K=0.096  K=0.097  K=0.098  K=0.099    K=0.1  K=0.101  K=0.102  K=0.103 
24.66728 24.69662 24.72614 24.75574 24.78545 24.81528 24.84513 24.87518 
 K=0.104  K=0.105  K=0.106  K=0.107  K=0.108  K=0.109   K=0.11  K=0.111 
24.90530 24.93543 24.96583 24.99619 25.02666 25.05721 25.08784 25.11860 
 K=0.112  K=0.113  K=0.114  K=0.115  K=0.116  K=0.117  K=0.118  K=0.119 
25.14937 25.18028 25.21119 25.24220 25.27332 25.30444 25.33565 25.36693 
  K=0.12  K=0.121  K=0.122  K=0.123  K=0.124  K=0.125  K=0.126  K=0.127 
25.39830 25.42968 25.46114 25.49263 25.52425 25.55584 25.58752 25.61929 
 K=0.128  K=0.129   K=0.13  K=0.131  K=0.132  K=0.133  K=0.134  K=0.135 
25.65105 25.68286 25.71468 25.74660 25.77856 25.81052 25.84256 25.87459 
 K=0.136  K=0.137  K=0.138  K=0.139   K=0.14  K=0.141  K=0.142  K=0.143 
25.90670 25.93884 25.97097 26.00315 26.03543 26.06763 26.09997 26.13228 
 K=0.144  K=0.145  K=0.146  K=0.147  K=0.148  K=0.149   K=0.15  K=0.151 
26.16459 26.19695 26.22930 26.26168 26.29412 26.32658 26.35903 26.39150 
 K=0.152  K=0.153  K=0.154  K=0.155  K=0.156  K=0.157  K=0.158  K=0.159 
26.42400 26.45651 26.48906 26.52161 26.55414 26.58674 26.61929 26.65191 
  K=0.16  K=0.161  K=0.162  K=0.163  K=0.164  K=0.165  K=0.166  K=0.167 
26.68447 26.71708 26.74974 26.78230 26.81495 26.84757 26.88019 26.91287 
 K=0.168  K=0.169   K=0.17  K=0.171  K=0.172  K=0.173  K=0.174  K=0.175 
26.94550 26.97817 27.01084 27.04347 27.07611 27.10880 27.14143 27.17409 
 K=0.176  K=0.177  K=0.178  K=0.179   K=0.18  K=0.181  K=0.182  K=0.183 
27.20674 27.23939 27.27200 27.30463 27.33725 27.36989 27.40253 27.43510 
 K=0.184  K=0.185  K=0.186  K=0.187  K=0.188  K=0.189   K=0.19  K=0.191 
27.46771 27.50035 27.53291 27.56548 27.59809 27.63063 27.66320 27.69571 
 K=0.192  K=0.193  K=0.194  K=0.195  K=0.196  K=0.197  K=0.198  K=0.199 
27.72829 27.76082 27.79328 27.82576 27.85830 27.89074 27.92321 27.95568 
   K=0.2 
27.98813 
     K=0  K=0.001  K=0.002  K=0.003  K=0.004  K=0.005  K=0.006  K=0.007 
60.54843 59.58105 59.15690 58.91546 58.75782 58.64582 58.56170 58.49582 
 K=0.008  K=0.009   K=0.01  K=0.011  K=0.012  K=0.013  K=0.014  K=0.015 
58.44281 58.39917 58.36274 58.33192 58.30578 58.28339 58.26424 58.24788 
 K=0.016  K=0.017  K=0.018  K=0.019   K=0.02  K=0.021  K=0.022  K=0.023 
58.23386 58.22206 58.21214 58.20391 58.19735 58.19209 58.18829 58.18568 
 K=0.024  K=0.025  K=0.026  K=0.027  K=0.028  K=0.029   K=0.03  K=0.031 
58.18430 58.18394 58.18463 58.18634 58.18897 58.19238 58.19668 58.20185 
 K=0.032  K=0.033  K=0.034  K=0.035  K=0.036  K=0.037  K=0.038  K=0.039 
58.20779 58.21442 58.22172 58.22970 58.23850 58.24771 58.25769 58.26827 
  K=0.04  K=0.041  K=0.042  K=0.043  K=0.044  K=0.045  K=0.046  K=0.047 
58.27927 58.29103 58.30325 58.31590 58.32917 58.34289 58.35713 58.37180 
 K=0.048  K=0.049   K=0.05  K=0.051  K=0.052  K=0.053  K=0.054  K=0.055 
58.38690 58.40245 58.41842 58.43484 58.45163 58.46882 58.48640 58.50435 
 K=0.056  K=0.057  K=0.058  K=0.059   K=0.06  K=0.061  K=0.062  K=0.063 
58.52265 58.54130 58.56030 58.57963 58.59924 58.61927 58.63953 58.66018 
 K=0.064  K=0.065  K=0.066  K=0.067  K=0.068  K=0.069   K=0.07  K=0.071 
58.68105 58.70219 58.72362 58.74534 58.76739 58.78959 58.81208 58.83485 
 K=0.072  K=0.073  K=0.074  K=0.075  K=0.076  K=0.077  K=0.078  K=0.079 
58.85779 58.88103 58.90449 58.92817 58.95208 58.97615 59.00048 59.02494 
  K=0.08  K=0.081  K=0.082  K=0.083  K=0.084  K=0.085  K=0.086  K=0.087 
59.04966 59.07461 59.09968 59.12496 59.15044 59.17600 59.20182 59.22782 
 K=0.088  K=0.089   K=0.09  K=0.091  K=0.092  K=0.093  K=0.094  K=0.095 
59.25393 59.28020 59.30660 59.33321 59.35989 59.38681 59.41386 59.44097 
 K=0.096  K=0.097  K=0.098  K=0.099    K=0.1  K=0.101  K=0.102  K=0.103 
59.46826 59.49562 59.52321 59.55087 59.57865 59.60657 59.63450 59.66268 
 K=0.104  K=0.105  K=0.106  K=0.107  K=0.108  K=0.109   K=0.11  K=0.111 
59.69091 59.71915 59.74772 59.77622 59.80485 59.83357 59.86237 59.89134 
 K=0.112  K=0.113  K=0.114  K=0.115  K=0.116  K=0.117  K=0.118  K=0.119 
59.92030 59.94943 59.97855 60.00778 60.03716 60.06651 60.09598 60.12552 
  K=0.12  K=0.121  K=0.122  K=0.123  K=0.124  K=0.125  K=0.126  K=0.127 
60.15518 60.18483 60.21459 60.24437 60.27431 60.30421 60.33422 60.36434 
 K=0.128  K=0.129   K=0.13  K=0.131  K=0.132  K=0.133  K=0.134  K=0.135 
60.39444 60.42460 60.45477 60.48507 60.51540 60.54574 60.57617 60.60659 
 K=0.136  K=0.137  K=0.138  K=0.139   K=0.14  K=0.141  K=0.142  K=0.143 
60.63712 60.66768 60.69822 60.72882 60.75955 60.79018 60.82099 60.85176 
 K=0.144  K=0.145  K=0.146  K=0.147  K=0.148  K=0.149   K=0.15  K=0.151 
60.88252 60.91336 60.94418 60.97504 61.00598 61.03694 61.06789 61.09887 
 K=0.152  K=0.153  K=0.154  K=0.155  K=0.156  K=0.157  K=0.158  K=0.159 
61.12989 61.16093 61.19201 61.22311 61.25418 61.28533 61.31643 61.34762 
  K=0.16  K=0.161  K=0.162  K=0.163  K=0.164  K=0.165  K=0.166  K=0.167 
61.37874 61.40993 61.44118 61.47232 61.50357 61.53477 61.56599 61.59730 
 K=0.168  K=0.169   K=0.17  K=0.171  K=0.172  K=0.173  K=0.174  K=0.175 
61.62853 61.65983 61.69113 61.72239 61.75366 61.78501 61.81629 61.84760 
 K=0.176  K=0.177  K=0.178  K=0.179   K=0.18  K=0.181  K=0.182  K=0.183 
61.87891 61.91023 61.94150 61.97280 62.00410 62.03543 62.06676 62.09802 
 K=0.184  K=0.185  K=0.186  K=0.187  K=0.188  K=0.189   K=0.19  K=0.191 
62.12933 62.16069 62.19195 62.22323 62.25457 62.28583 62.31713 62.34836 
 K=0.192  K=0.193  K=0.194  K=0.195  K=0.196  K=0.197  K=0.198  K=0.199 
62.37969 62.41097 62.44217 62.47339 62.50471 62.53589 62.56713 62.59839 
   K=0.2 
62.62961 

lmridge documentation built on May 2, 2019, 5:57 a.m.