Table 2 Prediction Performance & Variable Selection for MLR with Shrinkage Priors

Prediction

Priors

MS1

MS2

MS3

MS4

MS5

MS6

MS7

N,P,J,m

400,4, 3, (-2,-1,0,1,2)’

250,4,3,(-2,-1,0,1,2)’

400,10, 3,0

1000,30, 3,0

500,50, 3,0

600,20, 5,0

300,400, 3,0

β

(β₁,β₂,β₃)^′,β₁=(−1.3,1.2,0,0,2)^′,β₂=(2,−1.5,0,0)^′,β₃=0

β₁=(−1.3,1.2,0,0,2)^′,β₂=(2,−1.5,0,0)^′,β₃=0

β₁ = β₂ = (-1.3,-1.2,-0.5,-0.5,2,0,0,0,0,0)’, β₃=0

β₁=(A₇,B₁₃,C₇,D₃)^′,A₇∼N(2,0.25),B₁₃=0,C₇∼N(2,0.25),D₃=0.β₂=(E₁₀,F₇,G₁₃),E₁₀=0,F₇∼N(2,0.25),G₁₃=0

β∼N(0,1)

β₁=(A₇,B₁₃,C₇,D₃)^′,A₇∼N(2,0.25),B₁₃=0,C₇∼N(2,0.25),D₃=0,β₂=(E₁₀,F₇,G₁₃),E₁₀=0,F₇∼N(2,0.25),G₁₃=0

\(\beta =\left (\begin {array}{l} {\underbrace {N(0,1),\dots,N(0,1)}_{30}},{\underbrace {0,\dots,0}_{170}},\\ {\underbrace {N(0,1),\dots,N(0,1)}_{30}},{\underbrace {0,\dots,0}_{170}} \end {array}\right)\)

Accuracy

Horseshoe

0.812(0.048)

0.812(0.047)

0.712(0.078)

0.873(0.022)

0.816(0.044)

0.760(0.034)

0.576(0.071)

Dirichlet Laplace

0.811(0.048)

0.811(0.050)

0.722(0.050)

0.875(0.023)

0.818(0.043)

0.759(0.034)

0.602(0.068)

Double Pareto

0.813(0.048)

0.812(0.046)

0.713(0.078)

0.873(0.021)

0.816(0.044)

0.760(0.034)

0.583(0.069)

Miss-classification Error

Horseshoe

0.188(0.048)

0.188(0.047)

0.282(0.052)

0.127(0.022)

0.184(0.044)

0.240(0.034)

0.424(0.071)

Dirichlet Laplace

0.189(0.048)

0.189(0.050)

0.278(0.050)

0.125(0.023)

0.182(0.043)

0.241(0.034)

0.398(0.068)

Double Pareto

0.187(0.048)

0.188(0.046)

0.281(0.052)

0.127(0.021)

0.184(0.044)

0.240(0.034)

0.417(0.069)

C-Entropy

Horseshoe

0.487(0.071)

0.491(0.069)

0.670(0.073)

0.327(0.031)

0.432(0.072)

0.632(0.060)

1.557(0.308)

Dirichlet Laplace

0.480(0.089)

0.488(0.097)

0.665(0.100)

0.313(0.056)

0.620(0.177)

0.677(0.101)

4.113(0.969)

Double Pareto

0.488(0.070)

0.492(0.069)

0.671(0.072)

0.330(0.030)

0.430(0.073)

0.634(0.059)

1.963(0.424)

AUC

Horseshoe

0.719(0.060)

0.731(0.065)

0.710(0.047)

0.877(0.029)

0.824(0.050)

0.771(0.030)

0.632(0.066)

Dirichlet Laplace

0.708(0.059)

0.713(0.072)

0.716(0.047)

0.884(0.026)

0.827(0.048)

0.767(0.039)

0.654(0.062)

Double Pareto

0.720(0.059)

0.730(0.064)

0.713(0.048)

0.877(0.028)

0.825(0.048)

0.773(0.031)

0.636(0.065)

Variable Selection

Accuracy

Horseshoe

0.996(0.021)

0.970(0.057)

0.901(0.040)

0.986(0.015)

0.776(0.033)

0.754(0.039)

0.850(0.071)

Dirichlet Laplace

0.969(0.060)

0.934(0.091)

0.929(0.055)

0.954(0.026)

0.812(0.039)

0.789(0.048)

0.880(0.006)

Double Pareto

0.992(0.030)

0.976(0.052)

0.903(0.036)

0.986(0.014)

0.776(0.034)

0.749(0.039)

0.868(0.004)

Sensitivity

Horseshoe

0.998(0.025)

0.950(0.101)

0.838(0.056)

1.000(0.000)

0.675(0.045)

0.659(0.057)

0.052(0.021)

Dirichlet Laplace

0.970(0.082)

0.920(0.132)

0.936(0.069)

1.000(0.000)

0.849(0.046)

0.779(0.062)

0.237(0.033)

Double Pareto

0.998(0.025)

0.965(0.087)

0.838(0.053)

1.000(0.000)

0.677(0.047)

0.651(0.055)

0.122(0.026)

Specificity

Horseshoe

0.995(0.035)

0.990(0.049)

0.964(0.056)

0.978(0.024)

0.920(0.036)

0.875(0.051)

0.000(0.000)

Dirichlet Laplace

0.968(0.084)

0.948(0.125)

0.922(0.089)

0.929(0.040)

0.759(0.063)

0.803(0.075)

0.993(0.004)

Double Pareto

0.988(0.055)

0.988(0.055)

0.968(0.053)

0.979(0.022)

0.919(0.040)

0.875(0.049)

0.999(0.002)

L1 error

Horseshoe

0.255(0.035)

0.294(0.038)

0.275(0.024)

0.404(0.012)

0.335(0.013)

0.323(0.019)

0.006(0.006)

Dirichlet Laplace

0.215(0.077)

0.293(0.113)

0.206(0.060)

0.246(0.047)

0.550(0.035)

0.366(0.055)

0.024(0.024)

Double Pareto

0.260(0.035)

0.295(0.037)

0.281(0.024)

0.414(0.012)

0.328(0.014)

0.332(0.018)

0.011(0.011)

L2 error

Horseshoe

0.313(0.035)

0.358(0.037)

0.354(0.023)

0.582(0.009)

0.430(0.013)

0.409(0.018)

0.007(0.007)

Dirichlet Laplace

0.270(0.105)

0.366(0.149)

0.256(0.072)

0.313(0.064)

0.687(0.044)

0.464(0.067)

0.025(0.025)

Double Pareto

0.322(0.035)

0.363(0.037)

0.364(0.025)

0.601(0.010)

0.419(0.015)

0.420(0.017)

0.013(0.013)