Table 3 

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 parametersGriffing linear modelStandard normal modelOutlier model
Full modelBayesSpike:
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:
NameTrue value“a”“av”“Bambvw”“avw”“a”“Bambvw”“Bambvw”“Bambvw”“Bambvw”
μ77.52b7.52b7.23c7.35c7.28c7.447.32d7.41c7.4c7.25c7.49d
(−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)
a512.05−1.721.991.981.961.971.81.981.991.95
(−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)
a632.24−4.622.071.942.171.852.033.212.722.272.6
(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)
a777.865.467.617.657.637.697.596.957.217.417.16
(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)
a81211.277.2710.8610.7910.9610.8310.8510.7910.8210.8910.79
(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)
σ2120107.67105.09102.51102.28108.499.9h103.3863.5678.8991.7179.89
(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 falseFixedeB (0.381)B (0.376)B (0.247)B (0.233)B (0.296)B (0.34)B (0.268)
Randomfm (0.939)m (1.02)v (0.125)m (0.832)m (1.122)m (1.047)m (0.976)m (0.87)
Predict MSE119.66g122.5324.5124.7124.6122.5126.3124.3125.9125.2124.8124.9
(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 Embedded Image.

  • g Mean and 95% confidence interval of MSE from 1000 simulations (see main text).

  • h Confidence intervals were not available for the residual variance.