No. factors | R type | No. traits | Sample size | |||||||
---|---|---|---|---|---|---|---|---|---|---|

a | b | c | d | e | f | g | h | i | j | |

G and R | ||||||||||

No. traits | 100 | 100 | 100 | 100 | 100 | 20 | 1000 | 100 | 100 | 100 |

Residual type | SF^{a} | SF | SF | F^{b} | Wishart^{c} | SF | SF | SF | SF | SF |

No. factors | 10 | 25 | 50 | 10 | 5 | 10 | 10 | 10 | 10 | 10 |

h^{2} of factors^{d} | 0.5 (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. sires | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 50 | 100 | 500 |

No. offspring/sire | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 5 | 10 | 10 |

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 (*λ*) had a 75–97% chance of equaling zero._{ij}↵b Factor model for

**R**. Residual factors (those with ) were not sparse (*λ*≠ 0)._{ij}↵c

**R**was simulated from a Wishart distribution with*p*+ 1 degrees of freedom and inverse scale matrix . Five additional factors were each assigned a heritability of 1.0.↵d In each column, factors are divided between those

*h*^{2}> 0 and those with*h*^{2}= 0. The number in parentheses provides the number of factors with the given heritability.