[LONGITUDINAL]
input = {a,b}

EQUATION:
lp0 = a-b*t
lp1 = a-b*t/2
p0  = 1/(1+exp(-lp0))
p1  = 1/(1+exp(-lp1)) -p0
p2  = 1-p0-p1

DEFINITION:
y = {type       = categorical, 
     categories = {0, 1, 2},
     P(y=0)     = p0,
     P(y=1)     = p1}