Table 1.

Simulation Parameters

Parameters:
${\mathit{\beta }}_1={\left(-2.0,-0.1,-0.1,0.5\right)}^T$	${\mathbf{R}}^{\left(0\right)}={\mathbf{R}}^{\left(1\right)}$ (U):
${\mathit{\beta }}_2={\left(8.0,0.1,0.5,0.5\right)}^T$	$\left(\begin{array}{cccc}1.0& 0.2& 0.3& 0.5\\ 0.2& 1.0& 0.3& 0.1\\ 0.3& 0.3& 1.0& 0.1\\ 0.5& 0.1& 0.1& 1.0\end{array}\right)$
${\mathit{\beta }}_3={\left(-3.5,0.0,0.5,0.3\right)}^T$
${\mathit{\beta }}_4={\left(-1.0,0.1,-0.2,0.4\right)}^T$
${\mathit{\sigma }}^{2\left(0\right)}={\left(2.0,0.5,2.5,4.0\right)}^T$
${\mathit{\sigma }}^{2\left(1\right)}={\left(1.5,0.5,2.0,4.0\right)}^T$	${\mathbf{R}}^{\left(0\right)}={\mathbf{R}}^{\left(1\right)}$ (E): $\rho =0.25$

We set $\alpha \ge 0;$ simulated ${\mathbf{y}}_i$ were designed to correspond to actual data ${\mathbf{y}}_i={\left(-\sqrt{DURATION},\sqrt{INITIATION},-\sqrt{CPD},\sqrt{CESSATION}\right)}^T$; the covariate effects ${\mathit{\beta }}_j$ correspond to intercept, age (continuous), gender (0 = M, 1 = F), and college education (college graduate 0 = no, 1 = yes).