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Appendix D

# Model specification and SAS program for random coefficient multinomial logit model on health state among older Americans

The following random coefficient multinomial logit regression model is an extension of Equation (11.11). It is assumed that, in addition to the random effects on intercepts, the regression coefficients of time vary significantly over subjects, thereby specifying an extra random slope term. For analytic simplicity, the effects of time × time are assumed to remain fixed. Consequently, we have

$Pijk=Pr(Yij=kXij)=1+∑l=1Kexp(Xij′βl+b0il+b1ilTj+ɛijl)−1exp(Xij′βk+b0ik+b1ikTj+ɛijk) =1+∑l=1Kexp(Xij′βl)exp(b0il+b1ilTj+ɛijl)−1exp(Xij′βk)exp(b0ik+b1ikTj+ɛijk),$

(D.1)
where b0ik is the between-subjects random effect on the intercept ...

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