Parameter estimation processes of (a) RL model and (b) Prism-RL model tested with three different initial points A, B and C, and of (c) Prism-RL model with those in the infeasible region D, E and F. The yellowed area in the graph is the feasible region of the RL model.

Contexts in source publication

Context 1

... used all observations at once for this experiment. Again, as in the previous experiment, we set the true values of the parameters in (17) to ( , 3), we compared the estimation processes of the RL and Prism-RL models (Figure 3a,b). When the initial point was A (−4, 3), the RL and Prism-RL models both converged to the true value. ...

Context 2

... used all observations at once for this experiment. Again, as in the previous experiment, we set the true values of the parameters in (17) to ( , 3), we compared the estimation processes of the RL and Prism-RL models (Figure 3a,b). When the initial point was A (−4, 3), the RL and Prism-RL models both converged to the true value. ...

Context 3

... samples 1 and 3-10, we did not obtain results. diverged during the estimation process (blue and green trajectories in Figure 3a), because the parameters were updated to values in the infeasible region. In contrast, the Prism-RL model did not experience the numerical issue. ...

Context 4

... of the initial point, the Prism-RL model converged to the true value. The process appeared stable and no fluctuation or update to the RL infeasible region was not observed (Figure 3b). Moreover, we tested the estimation of the Prism-RL model with the initial point set to a value outside of the RL feasible region. ...

Context 5

... we tested the estimation of the Prism-RL model with the initial point set to a value outside of the RL feasible region. The result is shown in Figure 3(c). We tested three initial values D (1, 0), E (0, 2) and F (−1, 4), with which the RL model is infeasible due to the divergence of the value function. ...

Context 6

... tested three initial values D (1, 0), E (0, 2) and F (−1, 4), with which the RL model is infeasible due to the divergence of the value function. Figure 3(c) demonstrates that the Prism-RL model is feasible even with the parameters within the infeasible region of the RL model. This fact suggests the estimation stability of the Prism-RL model, since it is possible for the Prism-RL model to reach the solution even if the parameter is updated outside of the RL feasible region during the estimation process. ...

Context 7

... model performance was evaluated based on the log-likelihood obtained by applying the estimated model to the holdout sample: similarly to Mai et al. (2015), we computed the validation log-likelihood divided by the number of paths LL i = LL( ˆ β i ; σ i )/N i for each holdout sample i and then computed its average over samples Figure 4 shows the validation results, and Table 7 reports the average of the validation loglikelihood values over 10 holdout samples LL (= LL 10 ). As general observations, the NRL-based models (Models 2,5,7) had higher prediction performance than the RL-based models (Models 1,4,6), and the inclusion of positive attributes also improved model prediction performance (Models 3,6,7). ...