the ordered probit model with latent trait response is as follow:
An unobserved latent variable Y is distributed with mean μi and variance 1, where i refers to the respondent.
Yi ∼ N(μi, 1), i= 1, ...,N
μi = Zi'β, with covariates matrix Zi .
yi = k if t(k−1) ≤ Yi < t(k) ; for t(0) = −∞, t(5) = ∞, ∀ i & k = 1, ..., 5.
then,
F( t(1) − Zi'β), k= 1
F( t(2) − Zi'β) − F( t(1) − Zi'β), k= 2
Pr(yi = k) = F( t(3) − Zi'β) − F( t(2) − Zi'β), k= 3
F( t(4) − Zi'β) − F( t(3) − Zi'β), k= 4
1 − F( t(4) − Zi'β), k= 5,
where F(·) is the standard normal cumulative distribution function.
Which proc. should I use for this model? Genmod? How? Thanks a lot!