content_image/327616.jpg
<img src='content_image/327616.jpg'>

ership as the best long-term investment based on the covariates presented in Table 5. The MCMC results, presented in Table 6, are based on 15,000 iterations after a burn-in of 5,000 iterations with identical priors as in the simulations studies. With three outcomes, we have two cut-points and they are fixed at (0 , 3) for both the models across quantiles. Similar to the simulation studies, ( σ, γ ) is sampled using joint random-walk MH algorithm with tuning parameters ι$_{1}$ $_{= (}$√$_{3}$$_{.}$$_{0}$$_{,}$ √$_{2}$$_{.}$$_{4}$$_{,}$ √$_{4}$$_{.}$$_{4) to get an acceptance rate of approximately 33 percent}$ for the three considered quantiles. The inefficiency factor of the parameters are all less than 5 and trace plots of MCMC draws, as displayed in Figure 4 for the 75th quantile, show quick convergence. Trace plots at the other two quantiles are similar. 

The results presented in Table 6 clearly shows that the posterior estimates from FBQROR and BQROR models are fairly similar across all quantiles. Hence, we restrict our attention to 

