From: Quantile regression for overdispersed count data: a hierarchical method
 | No contamination (C = 0) | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.793 (0.769, 0.817) | −0.394 (−0.443,–0.346) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.791 (0.766, 0.817) | −0.393 (−0.441,–0.344) |
 Robust NB M-Estimation (Chambers et al.) | 0.755 (−, −) | −0.375 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.898 (0.863, 0.932) | −0.435 (−0.506,–0.364) |
 Poisson Log-Normal Regression | 0.79 (0.763, 0.816) | −0.396 (−0.444,–0.349) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.795 (0.77, 0.818) | −0.4 (−0.455,–0.351) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.793 (0.768, 0.819) | −0.402 (−0.456,–0.354) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.794 (0.77, 0.817) | −0.397 (−0.438,–0.352) |
 | C = 5 | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.67 (0.646, 0.695) | −0.352 (−0.398,–0.304) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.782 (0.754, 0.811) | −0.382 (−0.436,–0.327) |
 Robust NB M-Estimation (Chambers et al.) | 0.675 (−, −) | −0.35 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.858 (0.823, 0.892) | −0.436 (−0.508,–0.363) |
 Poisson Log-Normal Regression | 0.708 (0.681, 0.734) | −0.371 (−0.422,–0.319) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.746 (0.72, 0.773) | −0.384 (−0.432,–0.331) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.75 (0.722, 0.776) | −0.384 (−0.434,–0.329) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.748 (0.719, 0.774) | −0.386 (−0.436,–0.338) |
 | C = 10 | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.581 (0.555, 0.609) | −0.306 (−0.361,–0.249) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.816 (0.787, 0.845) | −0.418 (−0.473,–0.363) |
 Robust NB M-Estimation (Chambers et al.) | 0.677 (−, −) | −0.355 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.866 (0.832, 0.901) | −0.433 (−0.505,–0.361) |
 Poisson Log–Normal Regression | 0.711 (0.683, 0.741) | −0.374 (−0.431,–0.318) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.777 (0.749, 0.804) | −0.401 (−0.452,–0.346) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.776 (0.747, 0.805) | −0.401 (−0.459,–0.349) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.774 (0.744, 0.801) | −0.402 (−0.458,–0.344) |
 | C = 15 | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.512 (0.484, 0.539) | −0.304 (−0.359,–0.248) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.805 (0.776, 0.833) | −0.4 (−0.455,–0.346) |
 Robust NB M-Estimation (Chambers et al.) | 0.677 (−, −) | −0.36 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.861 (0.826, 0.897) | −0.436 (−0.508,–0.364) |
 Poisson Log-Normal Regression | 0.716 (0.686, 0.747) | −0.387 (−0.447,–0.325) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.785 (0.758, 0.813) | −0.405 (−0.463,–0.352) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.785 (0.757, 0.814) | −0.403 (−0.456,–0.346) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.786 (0.755, 0.817) | −0.408 (−0.461,–0.354) |
 | C = 20 | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.461 (0.43, 0.49) | −0.285 (−0.347,–0.223) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.794 (0.765, 0.822) | −0.395 (−0.448,–0.341) |
 Robust NB M-Estimation (Chambers et al.) | 0.69 (−, −) | −0.368 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.861 (0.826, 0.897) | −0.436 (−0.508,–0.364) |
 Poisson Log-Normal Regression | 0.727 (0.695, 0.761) | −0.396 (−0.46,–0.329) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.789 (0.757, 0.82) | −0.408 (−0.465,–0.349) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.791 (0.759, 0.821) | −0.407 (−0.468,–0.345) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.792 (0.762, 0.822) | −0.409 (−0.466,–0.348) |
 | C = 25 | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.421 (0.39, 0.452) | −0.27 (−0.329,–0.205) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.788 (0.76, 0.816) | −0.394 (−0.448,–0.34) |
 Robust NB M-Estimation (Chambers et al.) | 0.697 (−, −) | −0.374 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.861 (0.826, 0.897) | −0.436 (−0.508,–0.364) |
 Poisson Log-Normal Regression | 0.736 (0.701, 0.773) | −0.4 (−0.468,–0.333) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.797 (0.765, 0.83) | −0.41 (−0.472,–0.355) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.796 (0.765, 0.828) | −0.412 (−0.47,–0.357) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.797 (0.767, 0.827) | −0.411 (−0.468,–0.356) |
 | C = 30 | |
X1 | X2 | |
Generating Regression Parameters | 0.8 | −0.4 |
Predictor Effects (Mean, 95% CRI or CI), Estimation via: | ||
 Negative Binomial Regression | 0.388 (0.356, 0.419) | −0.256 (−0.326,–0.188) |
 Robust NB M-Estimation (Aeberhard et al.) | 0.786 (0.758, 0.815) | −0.394 (−0.447,–0.34) |
 Robust NB M-Estimation (Chambers et al.) | 0.703 (−, −) | −0.378 (−, −) |
 Count Jittering (Machados & Santos Silva) | 0.861 (0.826, 0.897) | −0.436 (−0.508,–0.364) |
 Poisson Log-Normal Regression | 0.741 (0.705, 0.776) | −0.403 (−0.471,–0.336) |
 Hierarchical Median Regression, PLN, Gamma Prior | 0.8 (0.769, 0.83) | −0.415 (−0.476,–0.354) |
 Hierarchical Median Regression, PLN, Uniform Prior | 0.798 (0.765, 0.83) | −0.409 (−0.469,–0.344) |
 Hierarchical Median Regression, PLN, Exponential Mean Prior | 0.798 (0.768, 0.83) | −0.41 (−0.467,–0.349) |