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ROC Curve Demo. Say 1. Say 0. %1s. 1. 0. | |. %0s. |<-logits of the 1s->|. |. |<-logits of the 0s->|. Say 1. Say 0. Say 1. Say 0. Say 1. Say 0. Say 1. Say 0. Say 1. Say 0. Say 1. Say 0.

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Say

1

Say

0

%1s

1

0

| |

%0s

|<-logits of the 1s->|

|

|<-logits of the 0s->|


Say

1

Say

0


Say

1

Say

0


Say

1

Say

0


Say

1

Say

0


Say

1

Say

0


Say

1

Say

0


Say

1

Say

0


Example 2

Example 2

0 1

Say 1

Say 0

X=10

X=13

X=16

1 - specificity


Example 21

Example 2

0 1

X=10

X=13

X=16

Say 1

Say 0

(2/25, 18/35)

1 - specificity


Example 22

Example 2

0 1

X=10

X=13

X=16

(10/25, 30/35)

(2/25, 18/35)

Say 1

Say 0

1 - specificity


Example 23

Example 2

0 1

X=10

X=13

X=16

(10/25, 30/35)

(1, 1)

(2/25, 18/35)

Say 1

Say 0

1 - specificity


Example 24

Example 2

0 1

X=10

X=13

X=16

Tie Tie

Say 1

Say 0

18 x 23

1 - specificity


Example 25

Example 2

0 1

X=10

X=13

X=16

Tie Tie

15 x 12

Tie

Tie Tie

Say 1

Say 0

18 x 23

Tie

1 - specificity


Example 26

Example 2

0 1

X=10

X=13

X=16

15x5/2

Tie Tie

8x12/2

Tie

15 x 12

Tie

Tie Tie

2x18/2

18 x 23

Tie Tie

Say 1

Tie

Say 0

1 - specificity

AUC Area Under Curve = concordant pair plus ½ ties (proportions)

Pairs: 25x35=875 with 0 paired with 1.

Proportion Concordant: (18x23+12x15)/(25x35)=(18/25)x(23/35)+(12/25)x(15/35)

½ Proportion Ties ½(2x18 + 8x12 + 15x5)/(25x35)

AUC = 697.5/875 = 0.7971.


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