Discriminant Analysis - Statpower

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ˆ ˆ ⎛ x1+ x2 β′ x ⎞ i > β ′ ⎜ ⎟ (9) ⎝ 2 ⎠ Notice that the regression coefficients can all be multiplied by a common constant c without affecting the inequality. Moreover, the pooled estimate S of the common covariance matrix can be calculated as 1 S= A (10) N + N −2 1 2
so ˆβ in Equation (9) can be replaced by −1 −1 A ( x1− x 2) or a= S ( x1−x 2) , since either substitution involves eliminating a multiplicative constant. With that substitution, we get w ′ −1 = ax ′ = x −x S x (11) ( ) 1 2 which is known as the linear discriminant function. The cutoff point is halfway between the averages of w, or at
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: Recall that group 1 is associated w
Page 13 and 14: Of course, we could generate a diff
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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