liu: Liu Regression and Estimator
In liureg: Liu Regression with Liu Biasing Parameters and Statistics
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
Fits a linear Liu regression model after scaling regressors and returns an object of class "liu" (by calling liuest function), designed to be used in plotting method, testing of Liu coefficients and for computation of different Liu related statistics. The Liu biasing parameter d can be a scalar or a vector. This new biased estimator was first proposed by Liu (1993) <doi:10.1080/03610929308831027>.
Usage
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liu(formula, data, d = 1, scaling=c("centered", "sc", "scaled"), ...)
liuest(formula, data, d=1, scaling=c("centered", "sc", "scaled"), ...)
## Default S3 method:
liu(formula, data, d = 1, scaling=c("centered", "sc", "scaled"), ...)
## S3 method for class 'liu'
coef(object, ...)
## S3 method for class 'liu'
print(x, digits = max(5,getOption("digits") - 5), ...)
## S3 method for class 'liu'
fitted(object, ...)
Arguments
formula
Standard R formula expression, that is, a symbolic representation of the model to be fitted and has form response~predictors. For further details, see formula.
data
An optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which liu or liuest is called.
d
Liu biasing parameter (may be a vector).
scaling
The method to be used to scale the predictors. The scaling option "sc" scales the predictors to correlation form, such that the correlation matrix has unit diagonal elements. "scaled" option standardizes the predictors to have zero mean and unit variance. "centered" option centers the predictors.
object
A liu object, typically generated by a call to liu for fitted.liu, predict.liu, vcov.liu, residuals.liu, infocr.liu, coef.liu, summary.liu and press.liu functions.
x
An object of class liu (for the hatl.liu, lstats.liu, dest.liu, summary.liu, print.liu, print.summary.liu, print.dest, print.lstats, and plot.liu, plot.biasliu and plot.infoliu.
digits
Minimum number of significant digits to be used.
...
Additional arguments to be passed to or from other methods.
Details
liu or liuest function fits in Liu regression after scaling the regressors and centering the response. The liu is default a function that calls liuest for computation of Liu coefficients and returns an object of class "liu" designed to be used in plotting method, testing of Liu coefficients and for computation of different Liu related statistics. If intercept is present in the model, its coefficient is not penalized. However, intercept is estimated from the relation y=\overline{y}-β \overline{X}. print.liu tries to be smart about formatting of Liu coefficients.
Value
liu function returns an object of class "liu" after calling list of named objects from liuest function:
coef
A named vector of fitted coefficients.
call
The matched call.
Inter
Was an intercept included?
scaling
The scaling method used.
mf
Actual data used.
y
The centered response variable.
xs
The scaled matrix of predictors.
xm
The vector of means of the predictors.
terms
The terms object used.
xscale
Square root of sum of squared deviation from mean regarding the scaling option used in liu or liuest function as argument.
lfit
The fitted value of Liu regression for given biasing parameter d.
d
The Liu regression biasing parameter d which can be scalar or a vector.
Note
The function at the current form cannot handle missing values. The user has to take prior action with missing values before using this function.
Author(s)
Muhammad Imdad Ullah, Muhammad Aslam
References
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.
See Also
Liu model fitting liu, Liu residuals residuals.liu, Liu PRESS press.liu, Testing of Liu Coefficients summary.liu
Examples
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data(Hald)
mod<-liu(y~., data = as.data.frame(Hald), d = seq(0, 0.1, 0.01), scaling = "centered")
## Scaled Coefficients
mod$coef
## Re-Scaled Coefficients
coef(mod)
## Liu fitted values
fitted(mod)
## Liu predited values
predict(mod)
## Liu Residuals
residuals(mod)
## Liu trace
plot(mod)
## Liu Var-Cov matrix
vcov(mod)
## Liu biasing parameters by researchers
dest(mod)
## Liu related statistics
lstats(mod)
## list of objects from liuest function
liuest(y~., data = as.data.frame(Hald), d = seq(0, 0.1, 0.01), scaling = "centered")
Example output
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
X1 1.41348287 1.41485907 1.41623526 1.41761146 1.41898766 1.42036386
X2 0.38189878 0.38318147 0.38446416 0.38574685 0.38702953 0.38831222
X3 -0.03582438 -0.03444704 -0.03306971 -0.03169237 -0.03031503 -0.02893769
X4 -0.27031652 -0.26905396 -0.26779141 -0.26652885 -0.26526630 -0.26400374
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
X1 1.42174006 1.42311625 1.42449245 1.42586865 1.4272448
X2 0.38959491 0.39087760 0.39216029 0.39344297 0.3947257
X3 -0.02756035 -0.02618302 -0.02480568 -0.02342834 -0.0220510
X4 -0.26274119 -0.26147863 -0.26021608 -0.25895352 -0.2576910
Intercept X1 X2 X3 X4
d=0 75.01755 1.413483 0.3818988 -0.03582438 -0.2703165
d=0.01 74.89142 1.414859 0.3831815 -0.03444704 -0.2690540
d=0.02 74.76530 1.416235 0.3844642 -0.03306971 -0.2677914
d=0.03 74.63918 1.417611 0.3857468 -0.03169237 -0.2665289
d=0.04 74.51306 1.418988 0.3870295 -0.03031503 -0.2652663
d=0.05 74.38694 1.420364 0.3883122 -0.02893769 -0.2640037
d=0.06 74.26082 1.421740 0.3895949 -0.02756035 -0.2627412
d=0.07 74.13469 1.423116 0.3908776 -0.02618302 -0.2614786
d=0.08 74.00857 1.424492 0.3921603 -0.02480568 -0.2602161
d=0.09 73.88245 1.425869 0.3934430 -0.02342834 -0.2589535
d=0.1 73.75633 1.427245 0.3947257 -0.02205100 -0.2576910
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05 d=0.06
1 -17.01572 -17.01484 -17.01396 -17.01308 -17.01220 -17.01133 -17.01045
2 -22.51081 -22.51204 -22.51328 -22.51451 -22.51575 -22.51698 -22.51822
3 10.83619 10.83330 10.83042 10.82754 10.82465 10.82177 10.81889
4 -6.00983 -6.01069 -6.01155 -6.01241 -6.01327 -6.01414 -6.01500
5 0.21219 0.21233 0.21247 0.21261 0.21275 0.21289 0.21303
6 9.87783 9.87757 9.87730 9.87704 9.87678 9.87651 9.87625
7 8.71882 8.71889 8.71895 8.71902 8.71909 8.71916 8.71922
8 -19.83525 -19.83438 -19.83351 -19.83263 -19.83176 -19.83089 -19.83002
9 -3.54783 -3.54937 -3.55091 -3.55244 -3.55398 -3.55551 -3.55705
10 20.05532 20.05673 20.05813 20.05953 20.06093 20.06233 20.06373
11 -13.73082 -13.72965 -13.72848 -13.72732 -13.72615 -13.72498 -13.72381
12 16.78188 16.78310 16.78432 16.78554 16.78676 16.78799 16.78921
13 16.16802 16.16905 16.17009 16.17112 16.17215 16.17318 16.17422
d=0.07 d=0.08 d=0.09 d=0.1
1 -17.00957 -17.00869 -17.00781 -17.00693
2 -22.51945 -22.52069 -22.52192 -22.52316
3 10.81600 10.81312 10.81024 10.80735
4 -6.01586 -6.01672 -6.01758 -6.01844
5 0.21317 0.21331 0.21345 0.21359
6 9.87599 9.87572 9.87546 9.87520
7 8.71929 8.71936 8.71943 8.71949
8 -19.82915 -19.82828 -19.82740 -19.82653
9 -3.55858 -3.56012 -3.56166 -3.56319
10 20.06513 20.06653 20.06793 20.06933
11 -13.72265 -13.72148 -13.72031 -13.71914
12 16.79043 16.79165 16.79287 16.79409
13 16.17525 16.17628 16.17731 16.17835
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05 d=0.06
1 78.40736 78.40824 78.40911 78.40999 78.41087 78.41175 78.41263
2 72.91227 72.91103 72.90980 72.90856 72.90733 72.90610 72.90486
3 106.25926 106.25638 106.25350 106.25061 106.24773 106.24485 106.24196
4 89.41325 89.41239 89.41153 89.41066 89.40980 89.40894 89.40808
5 95.63527 95.63541 95.63555 95.63569 95.63583 95.63597 95.63611
6 105.30091 105.30064 105.30038 105.30012 105.29985 105.29959 105.29933
7 104.14189 104.14196 104.14203 104.14210 104.14217 104.14223 104.14230
8 75.58783 75.58870 75.58957 75.59044 75.59131 75.59219 75.59306
9 91.87524 91.87371 91.87217 91.87064 91.86910 91.86756 91.86603
10 115.47840 115.47980 115.48120 115.48260 115.48400 115.48540 115.48680
11 81.69226 81.69343 81.69459 81.69576 81.69693 81.69810 81.69926
12 112.20496 112.20618 112.20740 112.20862 112.20984 112.21106 112.21228
13 111.59110 111.59213 111.59316 111.59420 111.59523 111.59626 111.59729
d=0.07 d=0.08 d=0.09 d=0.1
1 78.41351 78.41439 78.41527 78.41615
2 72.90363 72.90239 72.90116 72.89992
3 106.23908 106.23620 106.23331 106.23043
4 89.40722 89.40636 89.40549 89.40463
5 95.63625 95.63639 95.63653 95.63667
6 105.29906 105.29880 105.29854 105.29827
7 104.14237 104.14244 104.14250 104.14257
8 75.59393 75.59480 75.59567 75.59654
9 91.86449 91.86296 91.86142 91.85988
10 115.48821 115.48961 115.49101 115.49241
11 81.70043 81.70160 81.70277 81.70393
12 112.21350 112.21472 112.21594 112.21716
13 111.59832 111.59936 111.60039 111.60142
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
1 0.09264302 0.09176419 0.09088537 0.09000654 0.08912771 0.08824889
2 1.38773119 1.38896589 1.39020058 1.39143528 1.39266997 1.39390467
3 -1.95926381 -1.95638055 -1.95349729 -1.95061403 -1.94773076 -1.94484750
4 -1.81324831 -1.81238683 -1.81152535 -1.81066387 -1.80980239 -1.80894091
5 0.26472874 0.26458900 0.26444927 0.26430954 0.26416981 0.26403008
6 3.89909238 3.89935589 3.89961939 3.89988289 3.90014640 3.90040990
7 -1.44189439 -1.44196214 -1.44202989 -1.44209763 -1.44216538 -1.44223313
8 -3.08782783 -3.08869944 -3.08957104 -3.09044265 -3.09131426 -3.09218586
9 1.22475642 1.22629235 1.22782828 1.22936421 1.23090014 1.23243607
10 0.42159811 0.42019761 0.41879711 0.41739661 0.41599611 0.41459561
11 2.10774235 2.10657476 2.10540717 2.10423958 2.10307200 2.10190441
12 1.09504061 1.09382010 1.09259958 1.09137906 1.09015855 1.08893803
13 -2.19109847 -2.19213082 -2.19316318 -2.19419553 -2.19522789 -2.19626025
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
1 0.08737006 0.08649124 0.08561241 0.08473358 0.08385476
2 1.39513936 1.39637406 1.39760875 1.39884345 1.40007814
3 -1.94196424 -1.93908097 -1.93619771 -1.93331445 -1.93043119
4 -1.80807943 -1.80721795 -1.80635647 -1.80549499 -1.80463351
5 0.26389034 0.26375061 0.26361088 0.26347115 0.26333142
6 3.90067340 3.90093690 3.90120041 3.90146391 3.90172741
7 -1.44230088 -1.44236862 -1.44243637 -1.44250412 -1.44257186
8 -3.09305747 -3.09392908 -3.09480068 -3.09567229 -3.09654390
9 1.23397200 1.23550793 1.23704386 1.23857979 1.24011573
10 0.41319511 0.41179460 0.41039410 0.40899360 0.40759310
11 2.10073682 2.09956923 2.09840165 2.09723406 2.09606647
12 1.08771752 1.08649700 1.08527649 1.08405597 1.08283545
13 -2.19729260 -2.19832496 -2.19935732 -2.20038967 -2.20142203
$`d=0`
X1 X2 X3 X4
X1 0.2753729 0.2439503 0.2710395 0.2411783
X2 0.2439503 0.2589659 0.2515646 0.2522639
X3 0.2710395 0.2515646 0.2805669 0.2475798
X4 0.2411783 0.2522639 0.2475798 0.2475877
$`d=0.01`
X1 X2 X3 X4
X1 0.2772320 0.2457575 0.2729319 0.2429533
X2 0.2457575 0.2607311 0.2534059 0.2539971
X3 0.2729319 0.2534059 0.2824945 0.2493882
X4 0.2429533 0.2539971 0.2493882 0.2492897
$`d=0.02`
X1 X2 X3 X4
X1 0.2790977 0.2475710 0.2748310 0.2447345
X2 0.2475710 0.2625025 0.2552537 0.2557365
X3 0.2748310 0.2552537 0.2844289 0.2512029
X4 0.2447345 0.2557365 0.2512029 0.2509977
$`d=0.03`
X1 X2 X3 X4
X1 0.2809698 0.2493909 0.2767367 0.2465221
X2 0.2493909 0.2642801 0.2571079 0.2574819
X3 0.2767367 0.2571079 0.2863701 0.2530241
X4 0.2465221 0.2574819 0.2530241 0.2527116
$`d=0.04`
X1 X2 X3 X4
X1 0.2828485 0.2512171 0.2786490 0.2483158
X2 0.2512171 0.2660639 0.2589687 0.2592333
X3 0.2786490 0.2589687 0.2883180 0.2548516
X4 0.2483158 0.2592333 0.2548516 0.2544315
$`d=0.05`
X1 X2 X3 X4
X1 0.2847337 0.2530497 0.2805679 0.2501158
X2 0.2530497 0.2678539 0.2608359 0.2609909
X3 0.2805679 0.2608359 0.2902726 0.2566854
X4 0.2501158 0.2609909 0.2566854 0.2561573
$`d=0.06`
X1 X2 X3 X4
X1 0.2866254 0.2548886 0.2824935 0.2519220
X2 0.2548886 0.2696500 0.2627096 0.2627545
X3 0.2824935 0.2627096 0.2922340 0.2585256
X4 0.2519220 0.2627545 0.2585256 0.2578892
$`d=0.07`
X1 X2 X3 X4
X1 0.2885236 0.2567339 0.2844257 0.2537345
X2 0.2567339 0.2714524 0.2645897 0.2645242
X3 0.2844257 0.2645897 0.2942022 0.2603722
X4 0.2537345 0.2645242 0.2603722 0.2596270
$`d=0.08`
X1 X2 X3 X4
X1 0.2904283 0.2585856 0.2863646 0.2555532
X2 0.2585856 0.2732609 0.2664763 0.2663000
X3 0.2863646 0.2664763 0.2961771 0.2622251
X4 0.2555532 0.2663000 0.2622251 0.2613707
$`d=0.09`
X1 X2 X3 X4
X1 0.2923395 0.2604436 0.2883100 0.2573781
X2 0.2604436 0.2750756 0.2683694 0.2680818
X3 0.2883100 0.2683694 0.2981587 0.2640844
X4 0.2573781 0.2680818 0.2640844 0.2631204
$`d=0.1`
X1 X2 X3 X4
X1 0.2942571 0.2623079 0.2902621 0.2592093
X2 0.2623079 0.2768964 0.2702690 0.2698697
X3 0.2902621 0.2702690 0.3001471 0.2659500
X4 0.2592093 0.2698697 0.2659500 0.2648760
Liu biasing parameter d
d values
dmm -5.91524
dcl -5.97369
dopt -1.47218
dILE -0.83461
min GCV at 0.00000
Liu Regression Statistics:
EDF Sigma2 CL VAR Bias^2 MSE F R2 adj-R2
d=0 9.0677 5.3010 5.5315 1.0625 0.0703 1.1328 125.8194 0.9823 0.9735
d=0.01 9.0663 5.3014 5.5355 1.0697 0.0689 1.1387 125.8114 0.9823 0.9735
d=0.02 9.0650 5.3017 5.5395 1.0770 0.0675 1.1445 125.8034 0.9823 0.9735
d=0.03 9.0637 5.3021 5.5436 1.0843 0.0661 1.1505 125.7956 0.9823 0.9735
d=0.04 9.0624 5.3024 5.5476 1.0917 0.0648 1.1565 125.7878 0.9823 0.9735
d=0.05 9.0611 5.3027 5.5517 1.0990 0.0634 1.1625 125.7801 0.9823 0.9735
d=0.06 9.0598 5.3030 5.5558 1.1064 0.0621 1.1685 125.7724 0.9823 0.9735
d=0.07 9.0585 5.3033 5.5599 1.1138 0.0608 1.1746 125.7649 0.9823 0.9735
d=0.08 9.0573 5.3037 5.5640 1.1212 0.0595 1.1807 125.7574 0.9823 0.9735
d=0.09 9.0560 5.3040 5.5681 1.1287 0.0582 1.1869 125.7500 0.9823 0.9735
d=0.1 9.0548 5.3043 5.5722 1.1362 0.0569 1.1931 125.7427 0.9823 0.9735
minimum MSE occurred at d = 0
$coef
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
X1 1.41348287 1.41485907 1.41623526 1.41761146 1.41898766 1.42036386
X2 0.38189878 0.38318147 0.38446416 0.38574685 0.38702953 0.38831222
X3 -0.03582438 -0.03444704 -0.03306971 -0.03169237 -0.03031503 -0.02893769
X4 -0.27031652 -0.26905396 -0.26779141 -0.26652885 -0.26526630 -0.26400374
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
X1 1.42174006 1.42311625 1.42449245 1.42586865 1.4272448
X2 0.38959491 0.39087760 0.39216029 0.39344297 0.3947257
X3 -0.02756035 -0.02618302 -0.02480568 -0.02342834 -0.0220510
X4 -0.26274119 -0.26147863 -0.26021608 -0.25895352 -0.2576910
$xscale
[1] 1 1 1 1
$xs
X1 X2 X3 X4
1 -0.4615385 -22.153846 -5.769231 30
2 -6.4615385 -19.153846 3.230769 22
3 3.5384615 7.846154 -3.769231 -10
4 3.5384615 -17.153846 -3.769231 17
5 -0.4615385 3.846154 -5.769231 3
6 3.5384615 6.846154 -2.769231 -8
7 -4.4615385 22.846154 5.230769 -24
8 -6.4615385 -17.153846 10.230769 14
9 -5.4615385 5.846154 6.230769 -8
10 13.5384615 -1.153846 -7.769231 -4
11 -6.4615385 -8.153846 11.230769 4
12 3.5384615 17.846154 -2.769231 -18
13 2.5384615 19.846154 -3.769231 -18
$Inter
[1] 1
$xm
X1 X2 X3 X4
7.461538 48.153846 11.769231 30.000000
$y
1 2 3 4 5 6
-16.9230769 -21.1230769 8.8769231 -7.8230769 0.4769231 13.7769231
7 8 9 10 11 12
7.2769231 -22.9230769 -2.3230769 20.4769231 -11.6230769 17.8769231
13
13.9769231
$scaling
[1] "centered"
$call
liuest(formula = y ~ ., data = as.data.frame(Hald), d = seq(0,
0.1, 0.01), scaling = "centered")
$d
[1] 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
$lfit
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
[1,] -17.0157199 -17.0148411 -17.0139623 -17.0130835 -17.0122046 -17.011326
[2,] -22.5108081 -22.5120428 -22.5132775 -22.5145122 -22.5157469 -22.516982
[3,] 10.8361869 10.8333036 10.8304204 10.8275371 10.8246538 10.821771
[4,] -6.0098286 -6.0106901 -6.0115516 -6.0124131 -6.0132745 -6.014136
[5,] 0.2121943 0.2123341 0.2124738 0.2126135 0.2127533 0.212893
[6,] 9.8778307 9.8775672 9.8773037 9.8770402 9.8767767 9.876513
[7,] 8.7188175 8.7188852 8.7189530 8.7190207 8.7190885 8.719156
[8,] -19.8352491 -19.8343775 -19.8335059 -19.8326343 -19.8317627 -19.830891
[9,] -3.5478333 -3.5493693 -3.5509052 -3.5524411 -3.5539771 -3.555513
[10,] 20.0553250 20.0567255 20.0581260 20.0595265 20.0609270 20.062327
[11,] -13.7308193 -13.7296517 -13.7284841 -13.7273165 -13.7261489 -13.724981
[12,] 16.7818825 16.7831030 16.7843235 16.7855440 16.7867645 16.787985
[13,] 16.1680215 16.1690539 16.1700863 16.1711186 16.1721510 16.173183
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
[1,] -17.0104470 -17.0095682 -17.0086893 -17.0078105 -17.0069317
[2,] -22.5182163 -22.5194510 -22.5206857 -22.5219204 -22.5231551
[3,] 10.8188873 10.8160041 10.8131208 10.8102375 10.8073543
[4,] -6.0149975 -6.0158590 -6.0167205 -6.0175819 -6.0184434
[5,] 0.2130327 0.2131725 0.2133122 0.2134519 0.2135917
[6,] 9.8762497 9.8759862 9.8757227 9.8754592 9.8751957
[7,] 8.7192240 8.7192917 8.7193594 8.7194272 8.7194949
[8,] -19.8300195 -19.8291478 -19.8282762 -19.8274046 -19.8265330
[9,] -3.5570489 -3.5585849 -3.5601208 -3.5616567 -3.5631926
[10,] 20.0637280 20.0651285 20.0665290 20.0679295 20.0693300
[11,] -13.7238137 -13.7226462 -13.7214786 -13.7203110 -13.7191434
[12,] 16.7892056 16.7904261 16.7916466 16.7928671 16.7940876
[13,] 16.1742157 16.1752480 16.1762804 16.1773127 16.1783451
$mf
y X1 X2 X3 X4
1 78.5 7 26 6 60
2 74.3 1 29 15 52
3 104.3 11 56 8 20
4 87.6 11 31 8 47
5 95.9 7 52 6 33
6 109.2 11 55 9 22
7 102.7 3 71 17 6
8 72.5 1 31 22 44
9 93.1 2 54 18 22
10 115.9 21 47 4 26
11 83.8 1 40 23 34
12 113.3 11 66 9 12
13 109.4 10 68 8 12
$terms
y ~ X1 + X2 + X3 + X4
attr(,"variables")
list(y, X1, X2, X3, X4)
attr(,"factors")
X1 X2 X3 X4
y 0 0 0 0
X1 1 0 0 0
X2 0 1 0 0
X3 0 0 1 0
X4 0 0 0 1
attr(,"term.labels")
[1] "X1" "X2" "X3" "X4"
attr(,"order")
[1] 1 1 1 1
attr(,"intercept")
[1] 1
attr(,"response")
[1] 1
attr(,".Environment")
<environment: R_GlobalEnv>
attr(,"predvars")
list(y, X1, X2, X3, X4)
attr(,"dataClasses")
y X1 X2 X3 X4
"numeric" "numeric" "numeric" "numeric" "numeric"
liureg documentation built on May 2, 2019, 8:34 a.m.
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
Fits a linear Liu regression model after scaling regressors and returns an object of class "liu" (by calling liuest function), designed to be used in plotting method, testing of Liu coefficients and for computation of different Liu related statistics. The Liu biasing parameter d can be a scalar or a vector. This new biased estimator was first proposed by Liu (1993) <doi:10.1080/03610929308831027>.
Usage
1 2 3 4 5 6 7 8 9 10 | liu(formula, data, d = 1, scaling=c("centered", "sc", "scaled"), ...)
liuest(formula, data, d=1, scaling=c("centered", "sc", "scaled"), ...)
## Default S3 method:
liu(formula, data, d = 1, scaling=c("centered", "sc", "scaled"), ...)
## S3 method for class 'liu'
coef(object, ...)
## S3 method for class 'liu'
print(x, digits = max(5,getOption("digits") - 5), ...)
## S3 method for class 'liu'
fitted(object, ...)
|
Arguments
formula |
Standard R formula expression, that is, a symbolic representation of the model to be fitted and has form |
data |
An optional data frame containing the variables in the model. If not found in data, the variables are taken from |
d |
Liu biasing parameter (may be a vector). |
scaling |
The method to be used to scale the predictors. The scaling option |
object |
A liu object, typically generated by a call to |
x |
An object of class |
digits |
Minimum number of significant digits to be used. |
... |
Additional arguments to be passed to or from other methods. |
Details
liu or liuest function fits in Liu regression after scaling the regressors and centering the response. The liu is default a function that calls liuest for computation of Liu coefficients and returns an object of class "liu" designed to be used in plotting method, testing of Liu coefficients and for computation of different Liu related statistics. If intercept is present in the model, its coefficient is not penalized. However, intercept is estimated from the relation y=\overline{y}-β \overline{X}. print.liu tries to be smart about formatting of Liu coefficients.
Value
liu function returns an object of class "liu" after calling list of named objects from liuest function:
coef |
A named vector of fitted coefficients. |
call |
The matched call. |
Inter |
Was an intercept included? |
scaling |
The scaling method used. |
mf |
Actual data used. |
y |
The centered response variable. |
xs |
The scaled matrix of predictors. |
xm |
The vector of means of the predictors. |
terms |
The |
xscale |
Square root of sum of squared deviation from mean regarding the scaling option used in |
lfit |
The fitted value of Liu regression for given biasing parameter d. |
d |
The Liu regression biasing parameter d which can be scalar or a vector. |
Note
The function at the current form cannot handle missing values. The user has to take prior action with missing values before using this function.
Author(s)
Muhammad Imdad Ullah, Muhammad Aslam
References
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.
See Also
Liu model fitting liu, Liu residuals residuals.liu, Liu PRESS press.liu, Testing of Liu Coefficients summary.liu
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | data(Hald)
mod<-liu(y~., data = as.data.frame(Hald), d = seq(0, 0.1, 0.01), scaling = "centered")
## Scaled Coefficients
mod$coef
## Re-Scaled Coefficients
coef(mod)
## Liu fitted values
fitted(mod)
## Liu predited values
predict(mod)
## Liu Residuals
residuals(mod)
## Liu trace
plot(mod)
## Liu Var-Cov matrix
vcov(mod)
## Liu biasing parameters by researchers
dest(mod)
## Liu related statistics
lstats(mod)
## list of objects from liuest function
liuest(y~., data = as.data.frame(Hald), d = seq(0, 0.1, 0.01), scaling = "centered")
|
Example output
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
X1 1.41348287 1.41485907 1.41623526 1.41761146 1.41898766 1.42036386
X2 0.38189878 0.38318147 0.38446416 0.38574685 0.38702953 0.38831222
X3 -0.03582438 -0.03444704 -0.03306971 -0.03169237 -0.03031503 -0.02893769
X4 -0.27031652 -0.26905396 -0.26779141 -0.26652885 -0.26526630 -0.26400374
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
X1 1.42174006 1.42311625 1.42449245 1.42586865 1.4272448
X2 0.38959491 0.39087760 0.39216029 0.39344297 0.3947257
X3 -0.02756035 -0.02618302 -0.02480568 -0.02342834 -0.0220510
X4 -0.26274119 -0.26147863 -0.26021608 -0.25895352 -0.2576910
Intercept X1 X2 X3 X4
d=0 75.01755 1.413483 0.3818988 -0.03582438 -0.2703165
d=0.01 74.89142 1.414859 0.3831815 -0.03444704 -0.2690540
d=0.02 74.76530 1.416235 0.3844642 -0.03306971 -0.2677914
d=0.03 74.63918 1.417611 0.3857468 -0.03169237 -0.2665289
d=0.04 74.51306 1.418988 0.3870295 -0.03031503 -0.2652663
d=0.05 74.38694 1.420364 0.3883122 -0.02893769 -0.2640037
d=0.06 74.26082 1.421740 0.3895949 -0.02756035 -0.2627412
d=0.07 74.13469 1.423116 0.3908776 -0.02618302 -0.2614786
d=0.08 74.00857 1.424492 0.3921603 -0.02480568 -0.2602161
d=0.09 73.88245 1.425869 0.3934430 -0.02342834 -0.2589535
d=0.1 73.75633 1.427245 0.3947257 -0.02205100 -0.2576910
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05 d=0.06
1 -17.01572 -17.01484 -17.01396 -17.01308 -17.01220 -17.01133 -17.01045
2 -22.51081 -22.51204 -22.51328 -22.51451 -22.51575 -22.51698 -22.51822
3 10.83619 10.83330 10.83042 10.82754 10.82465 10.82177 10.81889
4 -6.00983 -6.01069 -6.01155 -6.01241 -6.01327 -6.01414 -6.01500
5 0.21219 0.21233 0.21247 0.21261 0.21275 0.21289 0.21303
6 9.87783 9.87757 9.87730 9.87704 9.87678 9.87651 9.87625
7 8.71882 8.71889 8.71895 8.71902 8.71909 8.71916 8.71922
8 -19.83525 -19.83438 -19.83351 -19.83263 -19.83176 -19.83089 -19.83002
9 -3.54783 -3.54937 -3.55091 -3.55244 -3.55398 -3.55551 -3.55705
10 20.05532 20.05673 20.05813 20.05953 20.06093 20.06233 20.06373
11 -13.73082 -13.72965 -13.72848 -13.72732 -13.72615 -13.72498 -13.72381
12 16.78188 16.78310 16.78432 16.78554 16.78676 16.78799 16.78921
13 16.16802 16.16905 16.17009 16.17112 16.17215 16.17318 16.17422
d=0.07 d=0.08 d=0.09 d=0.1
1 -17.00957 -17.00869 -17.00781 -17.00693
2 -22.51945 -22.52069 -22.52192 -22.52316
3 10.81600 10.81312 10.81024 10.80735
4 -6.01586 -6.01672 -6.01758 -6.01844
5 0.21317 0.21331 0.21345 0.21359
6 9.87599 9.87572 9.87546 9.87520
7 8.71929 8.71936 8.71943 8.71949
8 -19.82915 -19.82828 -19.82740 -19.82653
9 -3.55858 -3.56012 -3.56166 -3.56319
10 20.06513 20.06653 20.06793 20.06933
11 -13.72265 -13.72148 -13.72031 -13.71914
12 16.79043 16.79165 16.79287 16.79409
13 16.17525 16.17628 16.17731 16.17835
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05 d=0.06
1 78.40736 78.40824 78.40911 78.40999 78.41087 78.41175 78.41263
2 72.91227 72.91103 72.90980 72.90856 72.90733 72.90610 72.90486
3 106.25926 106.25638 106.25350 106.25061 106.24773 106.24485 106.24196
4 89.41325 89.41239 89.41153 89.41066 89.40980 89.40894 89.40808
5 95.63527 95.63541 95.63555 95.63569 95.63583 95.63597 95.63611
6 105.30091 105.30064 105.30038 105.30012 105.29985 105.29959 105.29933
7 104.14189 104.14196 104.14203 104.14210 104.14217 104.14223 104.14230
8 75.58783 75.58870 75.58957 75.59044 75.59131 75.59219 75.59306
9 91.87524 91.87371 91.87217 91.87064 91.86910 91.86756 91.86603
10 115.47840 115.47980 115.48120 115.48260 115.48400 115.48540 115.48680
11 81.69226 81.69343 81.69459 81.69576 81.69693 81.69810 81.69926
12 112.20496 112.20618 112.20740 112.20862 112.20984 112.21106 112.21228
13 111.59110 111.59213 111.59316 111.59420 111.59523 111.59626 111.59729
d=0.07 d=0.08 d=0.09 d=0.1
1 78.41351 78.41439 78.41527 78.41615
2 72.90363 72.90239 72.90116 72.89992
3 106.23908 106.23620 106.23331 106.23043
4 89.40722 89.40636 89.40549 89.40463
5 95.63625 95.63639 95.63653 95.63667
6 105.29906 105.29880 105.29854 105.29827
7 104.14237 104.14244 104.14250 104.14257
8 75.59393 75.59480 75.59567 75.59654
9 91.86449 91.86296 91.86142 91.85988
10 115.48821 115.48961 115.49101 115.49241
11 81.70043 81.70160 81.70277 81.70393
12 112.21350 112.21472 112.21594 112.21716
13 111.59832 111.59936 111.60039 111.60142
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
1 0.09264302 0.09176419 0.09088537 0.09000654 0.08912771 0.08824889
2 1.38773119 1.38896589 1.39020058 1.39143528 1.39266997 1.39390467
3 -1.95926381 -1.95638055 -1.95349729 -1.95061403 -1.94773076 -1.94484750
4 -1.81324831 -1.81238683 -1.81152535 -1.81066387 -1.80980239 -1.80894091
5 0.26472874 0.26458900 0.26444927 0.26430954 0.26416981 0.26403008
6 3.89909238 3.89935589 3.89961939 3.89988289 3.90014640 3.90040990
7 -1.44189439 -1.44196214 -1.44202989 -1.44209763 -1.44216538 -1.44223313
8 -3.08782783 -3.08869944 -3.08957104 -3.09044265 -3.09131426 -3.09218586
9 1.22475642 1.22629235 1.22782828 1.22936421 1.23090014 1.23243607
10 0.42159811 0.42019761 0.41879711 0.41739661 0.41599611 0.41459561
11 2.10774235 2.10657476 2.10540717 2.10423958 2.10307200 2.10190441
12 1.09504061 1.09382010 1.09259958 1.09137906 1.09015855 1.08893803
13 -2.19109847 -2.19213082 -2.19316318 -2.19419553 -2.19522789 -2.19626025
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
1 0.08737006 0.08649124 0.08561241 0.08473358 0.08385476
2 1.39513936 1.39637406 1.39760875 1.39884345 1.40007814
3 -1.94196424 -1.93908097 -1.93619771 -1.93331445 -1.93043119
4 -1.80807943 -1.80721795 -1.80635647 -1.80549499 -1.80463351
5 0.26389034 0.26375061 0.26361088 0.26347115 0.26333142
6 3.90067340 3.90093690 3.90120041 3.90146391 3.90172741
7 -1.44230088 -1.44236862 -1.44243637 -1.44250412 -1.44257186
8 -3.09305747 -3.09392908 -3.09480068 -3.09567229 -3.09654390
9 1.23397200 1.23550793 1.23704386 1.23857979 1.24011573
10 0.41319511 0.41179460 0.41039410 0.40899360 0.40759310
11 2.10073682 2.09956923 2.09840165 2.09723406 2.09606647
12 1.08771752 1.08649700 1.08527649 1.08405597 1.08283545
13 -2.19729260 -2.19832496 -2.19935732 -2.20038967 -2.20142203
$`d=0`
X1 X2 X3 X4
X1 0.2753729 0.2439503 0.2710395 0.2411783
X2 0.2439503 0.2589659 0.2515646 0.2522639
X3 0.2710395 0.2515646 0.2805669 0.2475798
X4 0.2411783 0.2522639 0.2475798 0.2475877
$`d=0.01`
X1 X2 X3 X4
X1 0.2772320 0.2457575 0.2729319 0.2429533
X2 0.2457575 0.2607311 0.2534059 0.2539971
X3 0.2729319 0.2534059 0.2824945 0.2493882
X4 0.2429533 0.2539971 0.2493882 0.2492897
$`d=0.02`
X1 X2 X3 X4
X1 0.2790977 0.2475710 0.2748310 0.2447345
X2 0.2475710 0.2625025 0.2552537 0.2557365
X3 0.2748310 0.2552537 0.2844289 0.2512029
X4 0.2447345 0.2557365 0.2512029 0.2509977
$`d=0.03`
X1 X2 X3 X4
X1 0.2809698 0.2493909 0.2767367 0.2465221
X2 0.2493909 0.2642801 0.2571079 0.2574819
X3 0.2767367 0.2571079 0.2863701 0.2530241
X4 0.2465221 0.2574819 0.2530241 0.2527116
$`d=0.04`
X1 X2 X3 X4
X1 0.2828485 0.2512171 0.2786490 0.2483158
X2 0.2512171 0.2660639 0.2589687 0.2592333
X3 0.2786490 0.2589687 0.2883180 0.2548516
X4 0.2483158 0.2592333 0.2548516 0.2544315
$`d=0.05`
X1 X2 X3 X4
X1 0.2847337 0.2530497 0.2805679 0.2501158
X2 0.2530497 0.2678539 0.2608359 0.2609909
X3 0.2805679 0.2608359 0.2902726 0.2566854
X4 0.2501158 0.2609909 0.2566854 0.2561573
$`d=0.06`
X1 X2 X3 X4
X1 0.2866254 0.2548886 0.2824935 0.2519220
X2 0.2548886 0.2696500 0.2627096 0.2627545
X3 0.2824935 0.2627096 0.2922340 0.2585256
X4 0.2519220 0.2627545 0.2585256 0.2578892
$`d=0.07`
X1 X2 X3 X4
X1 0.2885236 0.2567339 0.2844257 0.2537345
X2 0.2567339 0.2714524 0.2645897 0.2645242
X3 0.2844257 0.2645897 0.2942022 0.2603722
X4 0.2537345 0.2645242 0.2603722 0.2596270
$`d=0.08`
X1 X2 X3 X4
X1 0.2904283 0.2585856 0.2863646 0.2555532
X2 0.2585856 0.2732609 0.2664763 0.2663000
X3 0.2863646 0.2664763 0.2961771 0.2622251
X4 0.2555532 0.2663000 0.2622251 0.2613707
$`d=0.09`
X1 X2 X3 X4
X1 0.2923395 0.2604436 0.2883100 0.2573781
X2 0.2604436 0.2750756 0.2683694 0.2680818
X3 0.2883100 0.2683694 0.2981587 0.2640844
X4 0.2573781 0.2680818 0.2640844 0.2631204
$`d=0.1`
X1 X2 X3 X4
X1 0.2942571 0.2623079 0.2902621 0.2592093
X2 0.2623079 0.2768964 0.2702690 0.2698697
X3 0.2902621 0.2702690 0.3001471 0.2659500
X4 0.2592093 0.2698697 0.2659500 0.2648760
Liu biasing parameter d
d values
dmm -5.91524
dcl -5.97369
dopt -1.47218
dILE -0.83461
min GCV at 0.00000
Liu Regression Statistics:
EDF Sigma2 CL VAR Bias^2 MSE F R2 adj-R2
d=0 9.0677 5.3010 5.5315 1.0625 0.0703 1.1328 125.8194 0.9823 0.9735
d=0.01 9.0663 5.3014 5.5355 1.0697 0.0689 1.1387 125.8114 0.9823 0.9735
d=0.02 9.0650 5.3017 5.5395 1.0770 0.0675 1.1445 125.8034 0.9823 0.9735
d=0.03 9.0637 5.3021 5.5436 1.0843 0.0661 1.1505 125.7956 0.9823 0.9735
d=0.04 9.0624 5.3024 5.5476 1.0917 0.0648 1.1565 125.7878 0.9823 0.9735
d=0.05 9.0611 5.3027 5.5517 1.0990 0.0634 1.1625 125.7801 0.9823 0.9735
d=0.06 9.0598 5.3030 5.5558 1.1064 0.0621 1.1685 125.7724 0.9823 0.9735
d=0.07 9.0585 5.3033 5.5599 1.1138 0.0608 1.1746 125.7649 0.9823 0.9735
d=0.08 9.0573 5.3037 5.5640 1.1212 0.0595 1.1807 125.7574 0.9823 0.9735
d=0.09 9.0560 5.3040 5.5681 1.1287 0.0582 1.1869 125.7500 0.9823 0.9735
d=0.1 9.0548 5.3043 5.5722 1.1362 0.0569 1.1931 125.7427 0.9823 0.9735
minimum MSE occurred at d = 0
$coef
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
X1 1.41348287 1.41485907 1.41623526 1.41761146 1.41898766 1.42036386
X2 0.38189878 0.38318147 0.38446416 0.38574685 0.38702953 0.38831222
X3 -0.03582438 -0.03444704 -0.03306971 -0.03169237 -0.03031503 -0.02893769
X4 -0.27031652 -0.26905396 -0.26779141 -0.26652885 -0.26526630 -0.26400374
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
X1 1.42174006 1.42311625 1.42449245 1.42586865 1.4272448
X2 0.38959491 0.39087760 0.39216029 0.39344297 0.3947257
X3 -0.02756035 -0.02618302 -0.02480568 -0.02342834 -0.0220510
X4 -0.26274119 -0.26147863 -0.26021608 -0.25895352 -0.2576910
$xscale
[1] 1 1 1 1
$xs
X1 X2 X3 X4
1 -0.4615385 -22.153846 -5.769231 30
2 -6.4615385 -19.153846 3.230769 22
3 3.5384615 7.846154 -3.769231 -10
4 3.5384615 -17.153846 -3.769231 17
5 -0.4615385 3.846154 -5.769231 3
6 3.5384615 6.846154 -2.769231 -8
7 -4.4615385 22.846154 5.230769 -24
8 -6.4615385 -17.153846 10.230769 14
9 -5.4615385 5.846154 6.230769 -8
10 13.5384615 -1.153846 -7.769231 -4
11 -6.4615385 -8.153846 11.230769 4
12 3.5384615 17.846154 -2.769231 -18
13 2.5384615 19.846154 -3.769231 -18
$Inter
[1] 1
$xm
X1 X2 X3 X4
7.461538 48.153846 11.769231 30.000000
$y
1 2 3 4 5 6
-16.9230769 -21.1230769 8.8769231 -7.8230769 0.4769231 13.7769231
7 8 9 10 11 12
7.2769231 -22.9230769 -2.3230769 20.4769231 -11.6230769 17.8769231
13
13.9769231
$scaling
[1] "centered"
$call
liuest(formula = y ~ ., data = as.data.frame(Hald), d = seq(0,
0.1, 0.01), scaling = "centered")
$d
[1] 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
$lfit
d=0 d=0.01 d=0.02 d=0.03 d=0.04 d=0.05
[1,] -17.0157199 -17.0148411 -17.0139623 -17.0130835 -17.0122046 -17.011326
[2,] -22.5108081 -22.5120428 -22.5132775 -22.5145122 -22.5157469 -22.516982
[3,] 10.8361869 10.8333036 10.8304204 10.8275371 10.8246538 10.821771
[4,] -6.0098286 -6.0106901 -6.0115516 -6.0124131 -6.0132745 -6.014136
[5,] 0.2121943 0.2123341 0.2124738 0.2126135 0.2127533 0.212893
[6,] 9.8778307 9.8775672 9.8773037 9.8770402 9.8767767 9.876513
[7,] 8.7188175 8.7188852 8.7189530 8.7190207 8.7190885 8.719156
[8,] -19.8352491 -19.8343775 -19.8335059 -19.8326343 -19.8317627 -19.830891
[9,] -3.5478333 -3.5493693 -3.5509052 -3.5524411 -3.5539771 -3.555513
[10,] 20.0553250 20.0567255 20.0581260 20.0595265 20.0609270 20.062327
[11,] -13.7308193 -13.7296517 -13.7284841 -13.7273165 -13.7261489 -13.724981
[12,] 16.7818825 16.7831030 16.7843235 16.7855440 16.7867645 16.787985
[13,] 16.1680215 16.1690539 16.1700863 16.1711186 16.1721510 16.173183
d=0.06 d=0.07 d=0.08 d=0.09 d=0.1
[1,] -17.0104470 -17.0095682 -17.0086893 -17.0078105 -17.0069317
[2,] -22.5182163 -22.5194510 -22.5206857 -22.5219204 -22.5231551
[3,] 10.8188873 10.8160041 10.8131208 10.8102375 10.8073543
[4,] -6.0149975 -6.0158590 -6.0167205 -6.0175819 -6.0184434
[5,] 0.2130327 0.2131725 0.2133122 0.2134519 0.2135917
[6,] 9.8762497 9.8759862 9.8757227 9.8754592 9.8751957
[7,] 8.7192240 8.7192917 8.7193594 8.7194272 8.7194949
[8,] -19.8300195 -19.8291478 -19.8282762 -19.8274046 -19.8265330
[9,] -3.5570489 -3.5585849 -3.5601208 -3.5616567 -3.5631926
[10,] 20.0637280 20.0651285 20.0665290 20.0679295 20.0693300
[11,] -13.7238137 -13.7226462 -13.7214786 -13.7203110 -13.7191434
[12,] 16.7892056 16.7904261 16.7916466 16.7928671 16.7940876
[13,] 16.1742157 16.1752480 16.1762804 16.1773127 16.1783451
$mf
y X1 X2 X3 X4
1 78.5 7 26 6 60
2 74.3 1 29 15 52
3 104.3 11 56 8 20
4 87.6 11 31 8 47
5 95.9 7 52 6 33
6 109.2 11 55 9 22
7 102.7 3 71 17 6
8 72.5 1 31 22 44
9 93.1 2 54 18 22
10 115.9 21 47 4 26
11 83.8 1 40 23 34
12 113.3 11 66 9 12
13 109.4 10 68 8 12
$terms
y ~ X1 + X2 + X3 + X4
attr(,"variables")
list(y, X1, X2, X3, X4)
attr(,"factors")
X1 X2 X3 X4
y 0 0 0 0
X1 1 0 0 0
X2 0 1 0 0
X3 0 0 1 0
X4 0 0 0 1
attr(,"term.labels")
[1] "X1" "X2" "X3" "X4"
attr(,"order")
[1] 1 1 1 1
attr(,"intercept")
[1] 1
attr(,"response")
[1] 1
attr(,".Environment")
<environment: R_GlobalEnv>
attr(,"predvars")
list(y, X1, X2, X3, X4)
attr(,"dataClasses")
y X1 X2 X3 X4
"numeric" "numeric" "numeric" "numeric" "numeric"
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