# Solved – How to incorporate costs (into logit model) of false positive, false negative, true positive, true negative if they are different costs

How to incorporate costs (into logit model) of false positive, false negative, true positive, true negative responses, if they are different costs ? Is it possible to do that on the level of likelihood function ?

Edition :
I see know that likeligooe function could be quite easily modified to incorporate costs, but then likelihood function become discontinuous :

y_i == 1 oraz f(x_i*B) > 0.5 cost = cost11
y_i == 1 oraz f(x_i*B) < 0.5 cost = cost10
y_i == 0 oraz f(x_i*B) > 0.5 cost = cost01
y_i == 0 oraz f(x_i*B) < 0.5 cost = cost00

non-modified likelihood function :
f(x_i*B)^y_i * ( 1 – f(x_i*B) ) ^ (1 – y_i)

modified likelihood function :

(cost11*positive(f(x_i*B)-0.5) + cost10*negative(f(x_i*B)-0.5) ) ^ y_i
*
(cost00*negative(f(x_i*B)-0.5) + cost01*positive(f(x_i*B)-0.5) ) ^ (1 – y_i)

where :
positive(x) = 1 if x > 0
positive(x) = 0 if x < 0

negative(x) = 1 if x > 0
negative(x) = 0 if x < 0

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