Table 6: Posterior mean ( mean ) and standard deviation ( std ) of the parameters in the FBQROR and BQROR models for the homeownership application. 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 22 fbqror bqror 25th 50th 75th 25th 50th 75th mean std mean std mean std mean std mean std mean std intercept − 3 . 11 0 . 93 − 1 . 72 1 . 02 0 . 18 0 . 90 − 3 . 08 0 . 89 − 1 . 43 0 . 93 1 . 44 0 . 62 log age 0 . 52 0 . 17 0 . 60 0 . 17 0 . 55 0 . 16 0 . 18 0 . 16 0 . 63 0 . 17 0 . 47 0 . 12 log income 0 . 18 0 . 08 0 . 16 0 . 09 0 . 15 0 . 08 0 . 25 0 . 08 0 . 14 0 . 08 0 . 04 0 . 05 household size 0 . 01 0 . 04 0 . 01 0 . 04 0 . 01 0 . 04 − 0 . 01 0 . 04 0 . 01 0 . 04 0 . 02 0 . 03 female 0 . 64 0 . 14 0 . 62 0 . 14 0 . 54 0 . 13 0 . 57 0 . 13 0 . 57 0 . 13 0 . 32 0 . 09 post-bachelors − 0 . 83 0 . 22 − 0 . 86 0 . 22 − 0 . 81 0 . 20 − 0 . 50 0 . 21 − 0 . 86 0 . 21 − 0 . 62 0 . 15 bachelors 0 . 72 0 . 20 0 . 74 0 . 19 0 . 69 0 . 18 0 . 43 0 . 18 0 . 74 0 . 18 0 . 52 0 . 13 below bachelors − 0 . 37 0 . 17 − 0 . 36 0 . 17 − 0 . 33 0 . 16 − 0 . 26 0 . 16 − 0 . 34 0 . 16 − 0 . 25 0 . 12 full-time 0 . 04 0 . 16 0 . 02 0 . 16 0 . 02 0 . 14 0 . 09 0 . 15 0 . 01 0 . 15 0 . 01 0 . 10 part-time − 0 . 07 0 . 21 − 0 . 05 0 . 21 − 0 . 09 0 . 19 − 0 . 01 0 . 19 − 0 . 06 0 . 20 − 0 . 12 0 . 14 white 0 . 04 0 . 21 0 . 01 0 . 21 0 . 01 0 . 18 0 . 18 0 . 18 0 . 03 0 . 20 0 . 06 0 . 14 african-american 0 . 05 0 . 26 0 . 03 0 . 27 0 . 05 0 . 24 0 . 17 0 . 23 − 0 . 01 0 . 25 − 0 . 01 0 . 17 northeast 0 . 37 0 . 24 0 . 34 0 . 24 0 . 27 0 . 22 0 . 41 0 . 22 0 . 28 0 . 23 0 . 12 0 . 16 west 0 . 44 0 . 22 0 . 46 0 . 22 0 . 34 0 . 19 0 . 39 0 . 19 0 . 42 0 . 21 0 . 17 0 . 14 south 0 . 34 0 . 19 0 . 35 0 . 19 0 . 23 0 . 17 0 . 38 0 . 17 0 . 30 0 . 18 0 . 05 0 . 12 fin-worse − 0 . 45 0 . 16 − 0 . 48 0 . 16 − 0 . 43 0 . 14 − 0 . 34 0 . 15 − 0 . 46 0 . 15 − 0 . 31 0 . 11 fin-same 0 . 25 0 . 18 0 . 26 0 . 18 0 . 24 0 . 17 0 . 25 0 . 18 0 . 25 0 . 17 0 . 15 0 . 13 σ 0 . 89 0 . 13 1 . 07 0 . 05 0 . 83 0 . 08 0 . 88 0 . 03 1 . 06 0 . 04 0 . 59 0 . 02 γ 1 . 05 0 . 31 − 0 . 10 0 . 10 − 1 . 09 0 . 24 .. .. .. .. .. ..