Research Article

Mathematical Programming Approaches to Classification Problems

Table 6

The apparent, the LOO, and the holdout sample hit rates (in percentage) of the different models.

D1D2D3D4
NonnormalNonnormalNonnormalNonnormal
1 = 2 1 2 1 = 2 1 2
𝑛 1 = 2 1 , 𝑛 2 = 2 5 𝑛 1 = 2 2 , 𝑛 2 = 4 0 𝑛 1 = 5 0 , 𝑛 2 = 5 0 𝑛 1 = 4 4 4 , 𝑛 2 = 2 3 8
𝑛 = 4 6 𝑛 = 6 2 𝑛 = 1 0 0 𝑛 = 6 8 3
ApparentLOOApparentLOOApparentLOOApparentHoldout
hit ratehit ratehit ratehit ratehit rate
( 𝑛 = 6 8 3 )( 𝑛 = 1 8 3 )

LDF89,1 ( 5 )89,1 ( 5 )74,2 ( 1 6 )66,12 ( 2 1 )91 ( 9 )88 ( 1 2 )96,3 ( 2 5 )99,45 ( 1 )
LG91,3 ( 4 )89,1( 5 )74,2 ( 1 6 )66,12( 2 1 )93 ( 7 )88 ( 1 2 )96,9 ( 2 1 )98,9 ( 2 )
MSD89,1( 5 )89,1 ( 5 )75,8 ( 1 5 )66,12( 2 1 )91 ( 9 )84( 1 6 )96,6 ( 2 3 )95,6 ( 8 )
RS91,3 ( 4 )89,1 ( 5 )79 ( 1 3 )70,97 ( 1 8 )96 ( 4 )85 ( 1 5 )97,36 ( 1 8 )98,9 ( 2 )
MCA91,3 ( 4 )89,1 ( 5 )83,87 ( 1 0 )70,97 ( 1 8 ) 96 ( 4 )84 ( 1 6 )97,2 ( 1 9 )98,36 ( 3 )
MIPEDEADA91,3 ( 4 )89,1 ( 5 )85,4 ( 9 )75,8 ( 1 5 )96 ( 4 )91 ( 9 )97,2 ( 1 9 )98,9 ( 2 )
LPM89,1 ( 5 )89,1 ( 5 )74,2 ( 1 6 ) 66,12( 2 1 )93 ( 7 )84 ( 1 6 )96,6 ( 2 3 )96,7 ( 6 )
MC1 (LDF, LPM, RS)91,3( 4 )89,1 ( 5 )72,5 ( 1 7 )66,13 ( 2 1 )94 ( 6 )85 ( 1 5 )96,6 ( 2 3 )97,27 ( 5 )
MC2 (LDF, MSD, RS)91,3 ( 4 )89,1 ( 5 )69,35 ( 1 9 )64,5 ( 2 2 ) 94 ( 6 )84 ( 1 6 )96,3 ( 2 5 )96,7 ( 6 )

The values in parentheses are the numbers of misclassified observations.