chapter  29
8 Pages

Specific Regression Models

If assuming a standard normal distribution for L, the probability of a subject with covariate pattern x1,x2, . . . , xp to show Y = 1 is

P(Y = 1|x1,x2, . . . , xp) = P(L < β0 +β1x1 +β2x2 + . . . +βpxp) = Φ(β0 +β1x1 +β2x2 + . . . +βpxp)

with Φ denoting the distribution function of the standard normal distribution and hence

Φ−1(P(Y = 1|x1,x2, . . . , xp)) = β0 +β1x1 +β2x2 + . . . +βpxp .