Table 1 Simulation parameters
No. factorsR typeNo. traitsSample size
G and R
 No. traits100100100100100201000100100100
 Residual typeSFaSFSFFbWishartcSFSFSFSFSF
 No. factors1025501051010101010
 h2 of factorsd0.5 (5)0.5 (15)0.5 (30)0.5 (5)1.0 (5)0.5 (5)0.9–0.1 (5)
0.0 (5)0.0 (10)0.0 (20)0.0 (5)0.0 (5)0.0 (5)
Sample size
 No. sires10010010010010010010050100500
 No. offspring/sire1010101010101051010
  • Eight simulations were designed to demonstrate the capabilities of BSFG. Scenarios a–c test genetic and residual covariance matrices composed of different numbers of factors. Scenarios d–e test residual covariance matrices that are not sparse. Scenarios f–g test different numbers of traits. Scenarios h–j test different sample sizes. All simulations followed a paternal half-sib breeding design. Each simulation was run 10 times.

  • a Sparse factor model for R. Each simulated factor loading (λij) had a 75–97% chance of equaling zero.

  • b Factor model for R. Residual factors (those with Embedded Image) were not sparse (λij ≠ 0).

  • c R was simulated from a Wishart distribution with p + 1 degrees of freedom and inverse scale matrix Embedded Image. Five additional factors were each assigned a heritability of 1.0.

  • d In each column, factors are divided between those h2 > 0 and those with h2 = 0. The number in parentheses provides the number of factors with the given heritability.