[LONGITUDINAL]
input = {a,b}

EQUATION:
lp1 = a-b*t
lp2 = a-b*t/2
p1  = 1/(1+exp(-lp1))
p2  = 1/(1+exp(-lp2)) -p1
p3  = 1-p2-p1

DEFINITION:
y = {type       = categorical, 
     categories = {1,2,3},
     P(y=1)     = p1,
     P(y=2)     = p2}
