Performance of the No-U-Turn sampler in multi-trait variance component estimation using genomic data

Table 4 Estimated variance components, heritability and correlations in Scenario 2 using the real PIC pig data

Parameter	NUTS (LKJ prior)		NUTS (IW prior)		GS		REML
Parameter	Mean	SE	Mean	SE	Mean	SE	Estimate	SE
Additive (co)variances
\({\sigma }_{a}^{2}(T1)\)	0.02	0.01	0.13	0.04	0.01	0.01	0.02	0.01
\({\sigma }_{a}^{2}(T2)\)	0.34	0.07	0.34	0.07	0.38	0.08	0.28	0.06
\({\sigma }_{a}^{2}(T3)\)	0.28	0.08	0.30	0.08	0.35	0.09	0.31	0.09
\({\sigma }_{a}(T1,T2)\)	0.01	0.02	0.01	0.09	0.04	0.03	0.04	0.03
\({\sigma }_{a}(T1,T3)\)	0.01	0.02	0.04	0.04	0.02	0.04	0.06	0.04
\({\sigma }_{a}(T2,T3)\)	0.05	0.05	0.05	0.05	0.06	0.06	0.06	0.06
Residual (co)variances
\({\sigma }_{e}^{2}(T1)\)	1.04	0.06	0.96	0.07	1.05	0.07	1.04	0.06
\({\sigma }_{e}^{2}(T2)\)	0.60	0.06	0.59	0.06	0.58	0.06	0.69	0.04
\({\sigma }_{e}^{2}(T3)\)	0.67	0.07	0.65	0.07	0.64	0.07	0.65	0.07
\({\sigma }_{e}(T1,T2)\)	0.04	0.04	0.04	0.05	0.02	0.04	0.02	0.05
\({\sigma }_{e}(T1,T3)\)	0.00	0.04	− 0.02	0.08	0.00	0.05	− 0.07	0.04
\({\sigma }_{e}(T2,T3)\)	− 0.06	0.05	-0.06	0.02	− 0.07	0.05	− 0.07	0.05
Heritabilities
\({h}^{2}(T1)\)	0.02	0.02	0.12	0.04	0.01	0.01	0.01	0.01
\({h}^{2}(T2)\)	0.36	0.06	0.37	0.06	0.39	0.07	0.28	0.05
\({h}^{2}(T3)\)	0.29	0.07	0.32	0.08	0.35	0.08	0.32	0.08
Additive genetic correlations
\({r}_{a}(T1,T2)\)	0.13	0.32	0.05	0.20	0.62	0.44	0.63	0.53
\({r}_{a}(T1,T3)\)	0.12	0.36	0.19	0.23	0.32	0.48	0.88	0.53
\({r}_{a}(T2,T3)\)	0.15	0.16	0.16	0.17	0.16	0.17	0.21	0.21
Residual genetic correlations
\({r}_{e}(T1,T2)\)	0.05	0.05	0.05	0.06	0.02	0.06	0.02	0.05
\({r}_{e}(T1,T3)\)	0.00	0.05	− 0.02	0.11	− 0.02	0.09	− 0.09	0.05
\({r}_{e}(T2,T3)\)	− 0.09	0.06	− 0.10	0.04	− 0.11	0.08	− 0.12	0.08

NUTS No-U-Turn sampler, LKJ Lewandowski-Kurowicka-Joe, IW inverse-Wishart, GS Gibbs sampling, REML restricted maximum likelihood, SE standard error
\({\sigma }_{a}^{2}\): additive genetic variance, \({\sigma }_{a}\): additive genetic covariance, \({\sigma }_{e}^{2}\): residual variance, \({\sigma }_{e}\): residual covariance, \({h}^{2}\): heritability, \({r}_{a}\): additive genetic correlation, \({r}_{e}\): residual correlation

ISSN: 1297-9686