Performance of traditional and Bayesian models in inference and prediction for a simulated complete eight-way diallel with five replicates and additive effects
| BayesDiallel | ||||||||||||
| Simulated parameters | Griffing linear model | Standard normal model | Outlier model | |||||||||
| Full model | BayesSpike: | |||||||||||
| GCA: | GCA + SCA: | Full model: | Minimum DIC modela: | True model: | Full hglm fit: | BayesSpike: | d.f. = 3: | d.f. = 6: | d.f. = 15: | d.f. = 6: | ||
| Name | True value | “a” | “av” | “Bambvw” | “avw” | “a” | — | “Bambvw” | “Bambvw” | “Bambvw” | “Bambvw” | — |
| μ | 7 | 7.52b | 7.52b | 7.23c | 7.35c | 7.28c | 7.44 | 7.32d | 7.41c | 7.4c | 7.25c | 7.49d |
| (−4.94, 19.97) | (−90.92, 105.95) | (−2.72, 18.11) | (−3.65, 17.5) | (−3.46, 17.95) | (−2.51, 17.39) | (−2.6, 17.53) | (−3.91, 17.53) | (−3.71, 18) | (−2.84, 17.39) | (−2.14, 16.91) | ||
| a1 | −10 | −9.4 | −13.31 | −9.12 | −9.07 | −9.15 | −9.11 | −9.05 | −9.37 | −9.3 | −9.2 | −9.69 |
| (−11.61, −7.2) | (−17.8, −8.82) | (−11.43, −6.86) | (−11.18, −6.77) | (−11.5, −7.12) | (−14.6, −3.63) | (−11.28, −6.82) | (−11.75, −7.13) | (−11.68, −7.15) | (−11.52, −6.81) | (−11.5, −7.01) | ||
| a2 | −8 | −7.49 | −7.36 | −7.12 | −6.97 | −7.24 | −6.9 | −7.09 | −6.64 | −6.88 | −6.96 | −6.73 |
| (−9.69, −5.29) | (−11.85, −2.86) | (−9.5, −4.77) | (−9.37, −4.7) | (−9.3, −5.14) | (−12.38, −1.41) | (−9.38, −4.81) | (−8.88, −4.34) | (−9.2, −4.62) | (−9.1, −4.44) | (−9.11, −4.48) | ||
| a3 | −4 | −5.26 | −7.86 | −5.05 | −5 | −5.11 | −5 | −5.04 | −5.48 | −5.3 | −5.15 | −5.28 |
| (−7.46, −3.06) | (−12.35, −3.37) | (−7.21, −2.76) | (−7.1, −2.72) | (−7.26, −2.98) | (−10.48, 0.49) | (−7.4, −2.99) | (−7.96, −3.22) | (−7.56, −3.06) | (−7.68, −2.9) | (−7.57, −2.94) | ||
| a4 | −1 | −1.27 | −5.9 | −1.25 | −1.33 | −1.23 | −1.33 | −1.26 | −1.25 | −1.24 | −1.25 | −1.26 |
| (−3.47, 0.93) | (−10.39, −1.41) | (−3.52, 1) | (−3.63, 0.86) | (−3.3, 0.98) | (−6.81, 4.16) | (−3.43, 0.97) | (−3.55, 1.11) | (−3.53, 0.99) | (−3.61, 1.03) | (−3.42, 0.96) | ||
| a5 | 1 | 2.05 | −1.7 | 2 | 1.99 | 1.98 | 1.96 | 1.97 | 1.8 | 1.98 | 1.99 | 1.95 |
| (−0.15, 4.26) | (−6.2, 2.79) | (−0.27, 4.28) | (−0.26, 4.28) | (−0.23, 4.14) | (−3.53, 7.44) | (−0.23, 4.21) | (−0.6, 4.14) | (−0.21, 4.31) | (−0.25, 4.41) | (−0.31, 4.25) | ||
| a6 | 3 | 2.24 | −4.62 | 2.07 | 1.94 | 2.17 | 1.85 | 2.03 | 3.21 | 2.72 | 2.27 | 2.6 |
| (0.03, 4.44) | (−9.11, −0.13) | (−0.28, 4.3) | (−0.37, 4.22) | (0.14, 4.4) | (−3.63, 7.34) | (−0.21, 4.33) | (0.58, 5.74) | (0.18, 5.18) | (−0.21, 4.68) | (0.01, 4.83) | ||
| a7 | 7 | 7.86 | 5.46 | 7.61 | 7.65 | 7.63 | 7.69 | 7.59 | 6.95 | 7.21 | 7.41 | 7.16 |
| (5.66, 10.06) | (0.97, 9.95) | (5.22, 9.79) | (5.41, 9.9) | (5.61, 9.76) | (2.2, 13.17) | (5.22, 9.73) | (4.56, 9.29) | (4.8, 9.5) | (4.9, 9.6) | (4.86, 9.47) | ||
| a8 | 12 | 11.27 | 7.27 | 10.86 | 10.79 | 10.96 | 10.83 | 10.85 | 10.79 | 10.82 | 10.89 | 10.79 |
| (9.07, 13.47) | (2.78, 11.76) | (8.57, 13.21) | (8.39, 12.97) | (8.73, 13) | (5.35, 16.32) | (8.52, 13.07) | (8.38, 12.92) | (8.48, 13.1 | (8.56, 13.21) | (8.39, 12.98) | ||
| σ2 | 120 | 107.67 | 105.09 | 102.51 | 102.28 | 108.4 | 99.9h | 103.38 | 63.56 | 78.89 | 91.71 | 79.89 |
| (89.16, 126.17) | (86.05, 124.13) | (86.38, 118.92) | (85.76, 119.98) | (90.96, 125.84) | — | (86.16, 121.14) | (50.44, 77.27) | (64.87, 95.92) | (75.84, 107.49) | (66.35, 95.48) | ||
| Top false | Fixede | — | — | B (0.381) | — | — | B (0.376) | B (0.247) | B (0.233) | B (0.296) | B (0.34) | B (0.268) |
| Randomf | — | — | m (0.939) | m (1.02) | — | v (0.125) | m (0.832) | m (1.122) | m (1.047) | m (0.976) | m (0.87) | |
| Predict MSE | 119.66g | 122.5 | 324.5 | 124.7 | 124.6 | 122.5 | 126.3 | 124.3 | 125.9 | 125.2 | 124.8 | 124.9 |
| (111.28, 131.25) | (84.14, 166.45) | (243.59, 412.82) | (85.13, 169.98) | (85.35, 170.9) | (84.45, 166.14) | (86.96, 172.43) | (84.62, 169.96) | (85.89, 172.72) | (85.77, 171.32) | (85.42, 170.53) | (85.39, 170.81) | |
↵a “avw” is the model that minimized the DIC.
↵b Least-squares mean with 95% confidence interval in parentheses.
↵c Posterior mean with 95% posterior interval in parentheses.
↵d Posterior median with 95% posterior interval in parentheses.
↵e For BayesDiallel component q ∈ {βinbreed, …, τ2φw}, “q(x)” denotes p(q ≠ 0 | Data) for BayesSpike and min[p(β > 0 | Data), p(β < 0 | Data)] otherwise.
↵f Magnitude of the falsely included random-effects vector q averaged over T MCMC samples, as
.↵g Mean and 95% confidence interval of MSE from 1000 simulations (see main text).
↵h Confidence intervals were not available for the residual variance.
