The name is absent

r= 1, 2, 3, ∙ .4 Further, it is assumed that θ^f is distributed independently of the vector of
predictor variables z .

In the competing risks model, the joint survivor function for college completion
and college dropout, conditional on the two unobserved variables θ^g and θ^d, the vector of
predictor variables, x, and the waiting time until enrollment T^f is assumed to have the
following form:

k^g

S(kg,k^d∖x,θg,θ^d,T^f ) = exp[-θg∑ exp(γrg + (βg )'x + αT )

r =1
k^d

- θ ∑ exp(γd + (β^d )'x + αd T^f )]⁽²⁾
r=1

where the parameters γ^s_r are the baseline hazard parameters and the vector β^s_r measures
the (possibly time-varying) effects of the regressors, and α^s_r measures the (possibly time-
varying) effect of the waiting time until college enrollment, s = g, d, r=1, 2, 3,∙. Further,
it is assumed that θ^g and θ^d are distributed independently of the observed predictor
variables. The joint distribution of θ^f, θ^g, θ^d is denoted by G( θ^f, θ^g, θ^d). If θ^f is correlated
with θ^g and/or θ^d, then T^f will be correlated with θ^g and/or θ^d. However, we will jointly
estimate equations (1) and (2) using maximum likelihood estimation to explicitly account

⁴For simplicity of notation, the regressors are assumed to be time-constant. The model is easily extended
to the case of time-varying regressors although the notation is cumbersome.

10

<<   10   11   12   13   14   15   16   >>

More intriguing information