Table 1. Factor analytic models fitted to the dataset for genomic prediction. Increasing order factor models were assessed using AIC and log likelihood ratio tests comparing nested models. The model with additive: FA2 and residual genetic: FA2 covariance structure shows a significant improvement in fit from both additive: FA1 / residual genetic: FA1 and additive: FA1 / residual genetic: FA2 models and is referred to as the final model. Higher order models were not possible to fit with the computing resources available.

Covariance structure - Additive	Covariance structure - Residual genetic	REML Log Likelihood	AIC	Parameters	Full / reduced model parameters difference	Log likelihood ratio test model comparison:	Critical value	P value
DIAG	DIAG	4037.480	−8042.956	16	—	—	—	—
FA1	FA1	4405.638	−8747.276	32	16	to DIAG/DIAG	736.32	2.389×10−146
FA1	FA2	4465.921	−8853.842	39	7	to FA1/FA1	120.57	5.840×10−23
FA2	FA1	4453.568	−8829.136	39	7	to FA1/FA1	95.86	7.708×10−18
FA2	FA2	4473.418	−8854.836	46	7	to FA1/FA2	14.99	0.0361