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Table 6 Average posterior inference on marginal error (co)variances from ten replicates using the bivariate Student's-t (BSt) and normal (BN) fitted models with different residual degrees of freedom (DF).

From: Use of linear mixed models for genetic evaluation of gestation length and birth weight allowing for heavy-tailed residual effects

  

Fitted Model2

  

BS t

BN

True Parameters

True Model1

PM ± SE3

95% PPI4

ESS5

PM ± SE

95% PPI

ESS

= 30.0

BSt-4

30.45 ± 0.51

[27.44, 34.05]

3,336

30.29 ± 0.44

[28.61, 32.07]

42,430

= 18.0

BSt-12

17.87 ± 0.17

[16.75, 19.07]

9,516

17.82 ± 0.16

[16.83, 18.87]

43,135

= 15.0

BN-∞

14.94 ± 0.11

[14.10, 15.82]

43,387

14.94 ± 0.11

[14.11, 15.82]

43,204

= 8.0

BSt-4

8.20 ± 0.38

[6.45, 10.10]

11,384

8.37 ± 0.66

[6.95, 9.83]

44,553

= 4.8

BSt-12

4.61 ± 0.13

[3.69, 5.56]

32,416

4.57 ± 0.12

[3.72, 5.44]

44,370

= 4.0

BN-∞

3.94 ± 0.10

[3.23, 4.67]

43,729

3.94 ± 0.10

[3.23, 4.66]

44,238

= 40.0

BSt-4

40.07 ± 0.65

[35.98, 44.94]

3,566

39.57 ± 0.74

[37.37, 41.90]

45,168

= 24.0

BSt-12

24.60 ± 0.31

[23.04, 26.27]

10,145

24.54 ± 0.28

[23.17, 25.98]

45,130

= 20.0

BN-∞

20.13 ± 0.18

[19.00, 21.31]

42,782

20.12 ± 0.18

[19.00, 21.31]

45,079

  1. 1Used to simulate data
  2. 2Used in analysis of simulated data
  3. 3Posterior mean ± Standard Error
  4. 495% equal-tailed posterior probability interval based on the 2.5thand 97.5thpercentiles of the posterior density
  5. 5Effective sample size