Discriminant Analysis - Statpower

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′ ( x −1 −1 − x ) S ( x + x ) S ( x + x ) = a ′ (12) 2 2 1 2 1 2 1 2 So effectively, the classification rule becomes assign to population 1 if x −x ′ S x− x − x ′ S x + x > (13) −1 ( ) 1 −1 ( ) ( ) 1 2 2 1 2 1 2 0 and assign to population 2 otherwise.
Of course, we could generate a different discriminant function for each group and use a different decision rule: assign a subject to the group whose function value is higher. Equation (13) can be broken down into two formulae, and f f xS ′ x xS ′ x bx ′ (14) −1 1 −1 1 = 1 − 2 1 1 = 1 + a1 x ′ S x x ′ S x b ′ x (15) −1 1 −1 2 = 2 − 2 2 1 = 2 + a2
Page 1 and 2: Discriminant Analysis In discrimina
Page 3 and 4: Linear Discriminant Function - Two
Page 5 and 6: The linear discriminant function wa
Page 7 and 8: ( ) βˆ = cA −1 x −x (3) 1 2 w
Page 9 and 10: Recall that group 1 is associated w
Page 11: so ˆβ in Equation (9) can be repl
Page 15 and 16: above function values will lead to
Page 17 and 18: Example. Morrison (1990, page 143)
Page 19 and 20: In this case, −1 S is given by
Page 21 and 22: Note that variables x 1 and x 3 do
Page 23 and 24: But first, let’s perform the anal
Page 25 and 26: Now, if we drop the two non-contrib

Discriminant Analysis - Statpower

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