TABLE 2.

Simulation scenarios: data generating mechanisms.

	Data generating mechanism
General data generating mechanism	$U\sim N(0,0.1)$
	$L_0\sim N(U,1)$, $L_k\sim N({\delta }_0+{\delta }_L{L}_{k-1}+{\delta }_A{A}_{k-1}+{\delta }_{T}k+U,1)$ ($k=1,2,3,4$)
	$\text{logit}\mathrm{Pr}(A_0=1|L_0)={\gamma }_0+{\gamma }_L{L}_0$
	$\text{logit}\mathrm{Pr}(A_k=1|{\bar{A}}_{k-1},{\bar{L}}_k)={\gamma }_0+{\gamma }_A{A}_{k-1}+{\gamma }_L{L}_k$, ($k=1,2,3,4$)
	$h(k|{\bar{A}}_{\lfloor k\rfloor },{\bar{L}}_{\lfloor k\rfloor })={\alpha }_0+{\alpha }_A{A}_{\lfloor k\rfloor }+{\alpha }_L{L}_{\lfloor k\rfloor }+{\alpha }_{U}U$
Scenario 1	${\delta }_0=0,{\delta }_L=0.8,{\delta }_A=-1,{\delta }_T=0.1$
	${\gamma }_0=-1,{\gamma }_L=0.5$
	${\alpha }_0=0.2,{\alpha }_A=-0.04,{\alpha }_L=0.015,{\alpha }_U=0.015$
Scenario 2	${\delta }_0,{\delta }_L,{\delta }_A,{\delta }_T$: as in scenario 1
	${\gamma }_0=-3,{\gamma }_L=0.5$
	${\alpha }_0,{\alpha }_A,{\alpha }_L,{\alpha }_U$: as in scenario 1
Scenario 3	${\delta }_0,{\delta }_L,{\delta }_A,{\delta }_T$: as in scenario 1
	${\gamma }_0=-1,{\gamma }_L=3$
	${\alpha }_0,{\alpha }_A,{\alpha }_L,{\alpha }_U$: as in scenario 1