infoliu: Model Selection Criteria for Liu Regression
In liureg: Liu Regression with Liu Biasing Parameters and Statistics
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
The infoliu.liu computes model selection criteria (AIC and BIC).
Usage
1
2
3
Arguments
object
An object of class "liu".
...
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 degree of freedom df in the Liu regression model, using formula trace(H_d), where H_d is hat matrix from Liu regression. Model selection criteria may be helpful for selecting optimal value of biasing parameter d.
Value
It returns a matrix of information criteria, AIC and BIC for each biasing parameter d. Column of matrix indicates model selection criteria AIC and BIC, respectively, while rows indicate value of biasing parameter d 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. https://doi.org/10.1109/TAC.1974.1100705.
Akdeniz, F. and Kaciranlar, S. (1995). On the Almost Unbiased Generalized Liu Estimators and Unbiased Estimation of the Bias and MSE. Communications in Statistics-Theory and Methods, 24, 1789–1897. http://doi.org/10.1080/03610929508831585.
Imdad, M. U. (2017). Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan).
Imdadullah, M., Aslam, M., and Altaf, S. (2017). liureg: A comprehensive R Package for the Liu Estimation of Linear Regression Model with Collinear Regressors. The R Journal, 9 (2), 232–247.
Liu, K. (1993). A new Class of Biased Estimate in Linear Regression. Journal of Statistical Planning and Inference, 141, 189–196. http://doi.org/10.1080/03610929308831027.
Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461–464. https://projecteuclid.org/euclid.aos/1176344136.
See Also
Testing of Liu coefficient summary.liu
Examples
1
2
3
4
5
6
7
8
9
Example output
AIC BIC
d=-5 23.58670 58.28210
d=-4.9 23.58292 58.29347
d=-4.8 23.57985 58.30555
d=-4.7 23.57752 58.31835
d=-4.6 23.57592 58.33190
d=-4.5 23.57506 58.34619
d=-4.4 23.57497 58.36125
d=-4.3 23.57565 58.37707
d=-4.2 23.57710 58.39367
d=-4.1 23.57934 58.41106
d=-4 23.58239 58.42925
d=-3.9 23.58624 58.44824
d=-3.8 23.59091 58.46806
d=-3.7 23.59642 58.48871
d=-3.6 23.60276 58.51020
d=-3.5 23.60995 58.53254
d=-3.4 23.61800 58.55574
d=-3.3 23.62692 58.57980
d=-3.2 23.63672 58.60475
d=-3.1 23.64741 58.63058
d=-3 23.65900 58.65731
d=-2.9 23.67149 58.68495
d=-2.8 23.68489 58.71350
d=-2.7 23.69923 58.74298
d=-2.6 23.71449 58.77339
d=-2.5 23.73070 58.80474
d=-2.4 23.74785 58.83704
d=-2.3 23.76597 58.87030
d=-2.2 23.78505 58.90453
d=-2.1 23.80511 58.93973
d=-2 23.82615 58.97592
d=-1.9 23.84818 59.01310
d=-1.8 23.87121 59.05127
d=-1.7 23.89524 59.09045
d=-1.6 23.92029 59.13064
d=-1.5 23.94635 59.17185
d=-1.4 23.97344 59.21408
d=-1.3 24.00156 59.25735
d=-1.2 24.03072 59.30165
d=-1.1 24.06092 59.34700
d=-1 24.09217 59.39340
d=-0.899999999999999 24.12448 59.44085
d=-0.8 24.15785 59.48937
d=-0.7 24.19228 59.53895
d=-0.6 24.22779 59.58960
d=-0.5 24.26437 59.64132
d=-0.399999999999999 24.30202 59.69412
d=-0.3 24.34077 59.74801
d=-0.199999999999999 24.38059 59.80298
d=-0.0999999999999996 24.42151 59.85905
d=0 24.46352 59.91621
d=0.100000000000001 24.50663 59.97446
d=0.2 24.55084 60.03381
d=0.300000000000001 24.59615 60.09427
d=0.4 24.64256 60.15582
d=0.5 24.69007 60.21849
d=0.600000000000001 24.73870 60.28226
d=0.7 24.78843 60.34713
d=0.800000000000001 24.83927 60.41312
d=0.9 24.89123 60.48022
d=1 24.94429 60.54843
d=1.1 24.99846 60.61775
d=1.2 25.05374 60.68817
d=1.3 25.11014 60.75971
d=1.4 25.16764 60.83236
d=1.5 25.22625 60.90612
d=1.6 25.28597 60.98098
d=1.7 25.34679 61.05695
d=1.8 25.40872 61.13402
d=1.9 25.47175 61.21220
d=2 25.53587 61.29147
d=2.1 25.60110 61.37184
d=2.2 25.66742 61.45330
d=2.3 25.73482 61.53585
d=2.4 25.80332 61.61949
d=2.5 25.87289 61.70422
d=2.6 25.94355 61.79002
d=2.7 26.01528 61.87690
d=2.8 26.08808 61.96484
d=2.9 26.16195 62.05386
d=3 26.23688 62.14393
d=3.1 26.31286 62.23506
d=3.2 26.38989 62.32723
d=3.3 26.46797 62.42046
d=3.4 26.54708 62.51472
d=3.5 26.62723 62.61001
d=3.6 26.70840 62.70633
d=3.7 26.79059 62.80366
d=3.8 26.87379 62.90201
d=3.9 26.95800 63.00136
d=4 27.04321 63.10171
d=4.1 27.12940 63.20305
d=4.2 27.21658 63.30538
d=4.3 27.30473 63.40868
d=4.4 27.39385 63.51294
d=4.5 27.48393 63.61816
d=4.6 27.57496 63.72434
d=4.7 27.66693 63.83145
d=4.8 27.75983 63.93950
d=4.9 27.85366 64.04848
d=5 27.94840 64.15837
d=-5 d=-4.9 d=-4.8
23.58670 23.58292 23.57985
d=-4.7 d=-4.6 d=-4.5
23.57752 23.57592 23.57506
d=-4.4 d=-4.3 d=-4.2
23.57497 23.57565 23.57710
d=-4.1 d=-4 d=-3.9
23.57934 23.58239 23.58624
d=-3.8 d=-3.7 d=-3.6
23.59091 23.59642 23.60276
d=-3.5 d=-3.4 d=-3.3
23.60995 23.61800 23.62692
d=-3.2 d=-3.1 d=-3
23.63672 23.64741 23.65900
d=-2.9 d=-2.8 d=-2.7
23.67149 23.68489 23.69923
d=-2.6 d=-2.5 d=-2.4
23.71449 23.73070 23.74785
d=-2.3 d=-2.2 d=-2.1
23.76597 23.78505 23.80511
d=-2 d=-1.9 d=-1.8
23.82615 23.84818 23.87121
d=-1.7 d=-1.6 d=-1.5
23.89524 23.92029 23.94635
d=-1.4 d=-1.3 d=-1.2
23.97344 24.00156 24.03072
d=-1.1 d=-1 d=-0.899999999999999
24.06092 24.09217 24.12448
d=-0.8 d=-0.7 d=-0.6
24.15785 24.19228 24.22779
d=-0.5 d=-0.399999999999999 d=-0.3
24.26437 24.30202 24.34077
d=-0.199999999999999 d=-0.0999999999999996 d=0
24.38059 24.42151 24.46352
d=0.100000000000001 d=0.2 d=0.300000000000001
24.50663 24.55084 24.59615
d=0.4 d=0.5 d=0.600000000000001
24.64256 24.69007 24.73870
d=0.7 d=0.800000000000001 d=0.9
24.78843 24.83927 24.89123
d=1 d=1.1 d=1.2
24.94429 24.99846 25.05374
d=1.3 d=1.4 d=1.5
25.11014 25.16764 25.22625
d=1.6 d=1.7 d=1.8
25.28597 25.34679 25.40872
d=1.9 d=2 d=2.1
25.47175 25.53587 25.60110
d=2.2 d=2.3 d=2.4
25.66742 25.73482 25.80332
d=2.5 d=2.6 d=2.7
25.87289 25.94355 26.01528
d=2.8 d=2.9 d=3
26.08808 26.16195 26.23688
d=3.1 d=3.2 d=3.3
26.31286 26.38989 26.46797
d=3.4 d=3.5 d=3.6
26.54708 26.62723 26.70840
d=3.7 d=3.8 d=3.9
26.79059 26.87379 26.95800
d=4 d=4.1 d=4.2
27.04321 27.12940 27.21658
d=4.3 d=4.4 d=4.5
27.30473 27.39385 27.48393
d=4.6 d=4.7 d=4.8
27.57496 27.66693 27.75983
d=4.9 d=5
27.85366 27.94840
d=-5 d=-4.9 d=-4.8
58.28210 58.29347 58.30555
d=-4.7 d=-4.6 d=-4.5
58.31835 58.33190 58.34619
d=-4.4 d=-4.3 d=-4.2
58.36125 58.37707 58.39367
d=-4.1 d=-4 d=-3.9
58.41106 58.42925 58.44824
d=-3.8 d=-3.7 d=-3.6
58.46806 58.48871 58.51020
d=-3.5 d=-3.4 d=-3.3
58.53254 58.55574 58.57980
d=-3.2 d=-3.1 d=-3
58.60475 58.63058 58.65731
d=-2.9 d=-2.8 d=-2.7
58.68495 58.71350 58.74298
d=-2.6 d=-2.5 d=-2.4
58.77339 58.80474 58.83704
d=-2.3 d=-2.2 d=-2.1
58.87030 58.90453 58.93973
d=-2 d=-1.9 d=-1.8
58.97592 59.01310 59.05127
d=-1.7 d=-1.6 d=-1.5
59.09045 59.13064 59.17185
d=-1.4 d=-1.3 d=-1.2
59.21408 59.25735 59.30165
d=-1.1 d=-1 d=-0.899999999999999
59.34700 59.39340 59.44085
d=-0.8 d=-0.7 d=-0.6
59.48937 59.53895 59.58960
d=-0.5 d=-0.399999999999999 d=-0.3
59.64132 59.69412 59.74801
d=-0.199999999999999 d=-0.0999999999999996 d=0
59.80298 59.85905 59.91621
d=0.100000000000001 d=0.2 d=0.300000000000001
59.97446 60.03381 60.09427
d=0.4 d=0.5 d=0.600000000000001
60.15582 60.21849 60.28226
d=0.7 d=0.800000000000001 d=0.9
60.34713 60.41312 60.48022
d=1 d=1.1 d=1.2
60.54843 60.61775 60.68817
d=1.3 d=1.4 d=1.5
60.75971 60.83236 60.90612
d=1.6 d=1.7 d=1.8
60.98098 61.05695 61.13402
d=1.9 d=2 d=2.1
61.21220 61.29147 61.37184
d=2.2 d=2.3 d=2.4
61.45330 61.53585 61.61949
d=2.5 d=2.6 d=2.7
61.70422 61.79002 61.87690
d=2.8 d=2.9 d=3
61.96484 62.05386 62.14393
d=3.1 d=3.2 d=3.3
62.23506 62.32723 62.42046
d=3.4 d=3.5 d=3.6
62.51472 62.61001 62.70633
d=3.7 d=3.8 d=3.9
62.80366 62.90201 63.00136
d=4 d=4.1 d=4.2
63.10171 63.20305 63.30538
d=4.3 d=4.4 d=4.5
63.40868 63.51294 63.61816
d=4.6 d=4.7 d=4.8
63.72434 63.83145 63.93950
d=4.9 d=5
64.04848 64.15837
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
The infoliu.liu computes model selection criteria (AIC and BIC).
Usage
1 2 3 |
Arguments
object |
An object of class "liu". |
... |
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 degree of freedom df in the Liu regression model, using formula trace(H_d), where H_d is hat matrix from Liu regression. Model selection criteria may be helpful for selecting optimal value of biasing parameter d.
Value
It returns a matrix of information criteria, AIC and BIC for each biasing parameter d. Column of matrix indicates model selection criteria AIC and BIC, respectively, while rows indicate value of biasing parameter d 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. https://doi.org/10.1109/TAC.1974.1100705.
Akdeniz, F. and Kaciranlar, S. (1995). On the Almost Unbiased Generalized Liu Estimators and Unbiased Estimation of the Bias and MSE. Communications in Statistics-Theory and Methods, 24, 1789–1897. http://doi.org/10.1080/03610929508831585.
Imdad, M. U. (2017). Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan).
Imdadullah, M., Aslam, M., and Altaf, S. (2017). liureg: A comprehensive R Package for the Liu Estimation of Linear Regression Model with Collinear Regressors. The R Journal, 9 (2), 232–247.
Liu, K. (1993). A new Class of Biased Estimate in Linear Regression. Journal of Statistical Planning and Inference, 141, 189–196. http://doi.org/10.1080/03610929308831027.
Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461–464. https://projecteuclid.org/euclid.aos/1176344136.
See Also
Testing of Liu coefficient summary.liu
Examples
1 2 3 4 5 6 7 8 9 |
Example output
AIC BIC
d=-5 23.58670 58.28210
d=-4.9 23.58292 58.29347
d=-4.8 23.57985 58.30555
d=-4.7 23.57752 58.31835
d=-4.6 23.57592 58.33190
d=-4.5 23.57506 58.34619
d=-4.4 23.57497 58.36125
d=-4.3 23.57565 58.37707
d=-4.2 23.57710 58.39367
d=-4.1 23.57934 58.41106
d=-4 23.58239 58.42925
d=-3.9 23.58624 58.44824
d=-3.8 23.59091 58.46806
d=-3.7 23.59642 58.48871
d=-3.6 23.60276 58.51020
d=-3.5 23.60995 58.53254
d=-3.4 23.61800 58.55574
d=-3.3 23.62692 58.57980
d=-3.2 23.63672 58.60475
d=-3.1 23.64741 58.63058
d=-3 23.65900 58.65731
d=-2.9 23.67149 58.68495
d=-2.8 23.68489 58.71350
d=-2.7 23.69923 58.74298
d=-2.6 23.71449 58.77339
d=-2.5 23.73070 58.80474
d=-2.4 23.74785 58.83704
d=-2.3 23.76597 58.87030
d=-2.2 23.78505 58.90453
d=-2.1 23.80511 58.93973
d=-2 23.82615 58.97592
d=-1.9 23.84818 59.01310
d=-1.8 23.87121 59.05127
d=-1.7 23.89524 59.09045
d=-1.6 23.92029 59.13064
d=-1.5 23.94635 59.17185
d=-1.4 23.97344 59.21408
d=-1.3 24.00156 59.25735
d=-1.2 24.03072 59.30165
d=-1.1 24.06092 59.34700
d=-1 24.09217 59.39340
d=-0.899999999999999 24.12448 59.44085
d=-0.8 24.15785 59.48937
d=-0.7 24.19228 59.53895
d=-0.6 24.22779 59.58960
d=-0.5 24.26437 59.64132
d=-0.399999999999999 24.30202 59.69412
d=-0.3 24.34077 59.74801
d=-0.199999999999999 24.38059 59.80298
d=-0.0999999999999996 24.42151 59.85905
d=0 24.46352 59.91621
d=0.100000000000001 24.50663 59.97446
d=0.2 24.55084 60.03381
d=0.300000000000001 24.59615 60.09427
d=0.4 24.64256 60.15582
d=0.5 24.69007 60.21849
d=0.600000000000001 24.73870 60.28226
d=0.7 24.78843 60.34713
d=0.800000000000001 24.83927 60.41312
d=0.9 24.89123 60.48022
d=1 24.94429 60.54843
d=1.1 24.99846 60.61775
d=1.2 25.05374 60.68817
d=1.3 25.11014 60.75971
d=1.4 25.16764 60.83236
d=1.5 25.22625 60.90612
d=1.6 25.28597 60.98098
d=1.7 25.34679 61.05695
d=1.8 25.40872 61.13402
d=1.9 25.47175 61.21220
d=2 25.53587 61.29147
d=2.1 25.60110 61.37184
d=2.2 25.66742 61.45330
d=2.3 25.73482 61.53585
d=2.4 25.80332 61.61949
d=2.5 25.87289 61.70422
d=2.6 25.94355 61.79002
d=2.7 26.01528 61.87690
d=2.8 26.08808 61.96484
d=2.9 26.16195 62.05386
d=3 26.23688 62.14393
d=3.1 26.31286 62.23506
d=3.2 26.38989 62.32723
d=3.3 26.46797 62.42046
d=3.4 26.54708 62.51472
d=3.5 26.62723 62.61001
d=3.6 26.70840 62.70633
d=3.7 26.79059 62.80366
d=3.8 26.87379 62.90201
d=3.9 26.95800 63.00136
d=4 27.04321 63.10171
d=4.1 27.12940 63.20305
d=4.2 27.21658 63.30538
d=4.3 27.30473 63.40868
d=4.4 27.39385 63.51294
d=4.5 27.48393 63.61816
d=4.6 27.57496 63.72434
d=4.7 27.66693 63.83145
d=4.8 27.75983 63.93950
d=4.9 27.85366 64.04848
d=5 27.94840 64.15837
d=-5 d=-4.9 d=-4.8
23.58670 23.58292 23.57985
d=-4.7 d=-4.6 d=-4.5
23.57752 23.57592 23.57506
d=-4.4 d=-4.3 d=-4.2
23.57497 23.57565 23.57710
d=-4.1 d=-4 d=-3.9
23.57934 23.58239 23.58624
d=-3.8 d=-3.7 d=-3.6
23.59091 23.59642 23.60276
d=-3.5 d=-3.4 d=-3.3
23.60995 23.61800 23.62692
d=-3.2 d=-3.1 d=-3
23.63672 23.64741 23.65900
d=-2.9 d=-2.8 d=-2.7
23.67149 23.68489 23.69923
d=-2.6 d=-2.5 d=-2.4
23.71449 23.73070 23.74785
d=-2.3 d=-2.2 d=-2.1
23.76597 23.78505 23.80511
d=-2 d=-1.9 d=-1.8
23.82615 23.84818 23.87121
d=-1.7 d=-1.6 d=-1.5
23.89524 23.92029 23.94635
d=-1.4 d=-1.3 d=-1.2
23.97344 24.00156 24.03072
d=-1.1 d=-1 d=-0.899999999999999
24.06092 24.09217 24.12448
d=-0.8 d=-0.7 d=-0.6
24.15785 24.19228 24.22779
d=-0.5 d=-0.399999999999999 d=-0.3
24.26437 24.30202 24.34077
d=-0.199999999999999 d=-0.0999999999999996 d=0
24.38059 24.42151 24.46352
d=0.100000000000001 d=0.2 d=0.300000000000001
24.50663 24.55084 24.59615
d=0.4 d=0.5 d=0.600000000000001
24.64256 24.69007 24.73870
d=0.7 d=0.800000000000001 d=0.9
24.78843 24.83927 24.89123
d=1 d=1.1 d=1.2
24.94429 24.99846 25.05374
d=1.3 d=1.4 d=1.5
25.11014 25.16764 25.22625
d=1.6 d=1.7 d=1.8
25.28597 25.34679 25.40872
d=1.9 d=2 d=2.1
25.47175 25.53587 25.60110
d=2.2 d=2.3 d=2.4
25.66742 25.73482 25.80332
d=2.5 d=2.6 d=2.7
25.87289 25.94355 26.01528
d=2.8 d=2.9 d=3
26.08808 26.16195 26.23688
d=3.1 d=3.2 d=3.3
26.31286 26.38989 26.46797
d=3.4 d=3.5 d=3.6
26.54708 26.62723 26.70840
d=3.7 d=3.8 d=3.9
26.79059 26.87379 26.95800
d=4 d=4.1 d=4.2
27.04321 27.12940 27.21658
d=4.3 d=4.4 d=4.5
27.30473 27.39385 27.48393
d=4.6 d=4.7 d=4.8
27.57496 27.66693 27.75983
d=4.9 d=5
27.85366 27.94840
d=-5 d=-4.9 d=-4.8
58.28210 58.29347 58.30555
d=-4.7 d=-4.6 d=-4.5
58.31835 58.33190 58.34619
d=-4.4 d=-4.3 d=-4.2
58.36125 58.37707 58.39367
d=-4.1 d=-4 d=-3.9
58.41106 58.42925 58.44824
d=-3.8 d=-3.7 d=-3.6
58.46806 58.48871 58.51020
d=-3.5 d=-3.4 d=-3.3
58.53254 58.55574 58.57980
d=-3.2 d=-3.1 d=-3
58.60475 58.63058 58.65731
d=-2.9 d=-2.8 d=-2.7
58.68495 58.71350 58.74298
d=-2.6 d=-2.5 d=-2.4
58.77339 58.80474 58.83704
d=-2.3 d=-2.2 d=-2.1
58.87030 58.90453 58.93973
d=-2 d=-1.9 d=-1.8
58.97592 59.01310 59.05127
d=-1.7 d=-1.6 d=-1.5
59.09045 59.13064 59.17185
d=-1.4 d=-1.3 d=-1.2
59.21408 59.25735 59.30165
d=-1.1 d=-1 d=-0.899999999999999
59.34700 59.39340 59.44085
d=-0.8 d=-0.7 d=-0.6
59.48937 59.53895 59.58960
d=-0.5 d=-0.399999999999999 d=-0.3
59.64132 59.69412 59.74801
d=-0.199999999999999 d=-0.0999999999999996 d=0
59.80298 59.85905 59.91621
d=0.100000000000001 d=0.2 d=0.300000000000001
59.97446 60.03381 60.09427
d=0.4 d=0.5 d=0.600000000000001
60.15582 60.21849 60.28226
d=0.7 d=0.800000000000001 d=0.9
60.34713 60.41312 60.48022
d=1 d=1.1 d=1.2
60.54843 60.61775 60.68817
d=1.3 d=1.4 d=1.5
60.75971 60.83236 60.90612
d=1.6 d=1.7 d=1.8
60.98098 61.05695 61.13402
d=1.9 d=2 d=2.1
61.21220 61.29147 61.37184
d=2.2 d=2.3 d=2.4
61.45330 61.53585 61.61949
d=2.5 d=2.6 d=2.7
61.70422 61.79002 61.87690
d=2.8 d=2.9 d=3
61.96484 62.05386 62.14393
d=3.1 d=3.2 d=3.3
62.23506 62.32723 62.42046
d=3.4 d=3.5 d=3.6
62.51472 62.61001 62.70633
d=3.7 d=3.8 d=3.9
62.80366 62.90201 63.00136
d=4 d=4.1 d=4.2
63.10171 63.20305 63.30538
d=4.3 d=4.4 d=4.5
63.40868 63.51294 63.61816
d=4.6 d=4.7 d=4.8
63.72434 63.83145 63.93950
d=4.9 d=5
64.04848 64.15837
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