“…The traits (i.e., fractures) were analyzed using non‐linear categorical (threshold) trait models in the Gibbs Sampling Threshold Model (GSTM) program (Miyake, Oki, Nishiura, Ibi, & Sasaki, , based on Sorensen, Anderson, Gianola, & Korsgaard, ). This program has been used for categorical trait genetic analyses in dogs, racing pigeons, and Thoroughbred racehorses (Oki et al, ; Oki, Miyake, Kasashima, & Sasaki, ; Ramadan, Miyake, Yamaura, & Inoue‐Murayama, ; Ruefenacht, Gebhardt‐Henrich, Miyake, & Gaillard, ). The following model was used to perform a non‐linear categorical trait analysis:where L ijk is the normally distributed liability assumed with threshold t (Sorensen et al, ) behind the categorical phenotypes Y ijk of the categorized bone fracture.…”