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

Table 1 Estimated variance components, heritability and correlations in Scenario 1 using the simulated data

Parameter	True value	NUTS (LKJ prior)		NUTS (IW prior)		GS		REML
Parameter	True value	Mean	SE	Mean	SE	Mean	SE	Estimate	SE
Additive genetic (co)variances
\({\sigma }_{a}^{2}(trait1)\)	1.05	1.11	0.26	1.29	0.21	1.24	0.30	1.19	0.27
\({\sigma }_{a}^{2}(trait2)\)	5.14	5.04	0.44	5.02	0.48	5.47	0.47	5.37	0.49
\({\sigma }_{a}(trait1, trait2)\)	0.70	0.64	0.24	0.61	0.31	0.64	0.26	0.65	0.27
Residual (co)variances
\({\sigma }_{e}^{2}(trait1)\)	8.99	8.93	0.32	8.82	0.38	8.87	0.32	8.85	0.32
\({\sigma }_{e}^{2}(trait2)\)	5.03	4.96	0.22	4.96	0.26	4.70	0.24	4.70	0.24
\({\sigma }_{e}(trait1, trait2)\)	0.65	0.66	0.19	0.67	0.20	0.66	0.26	0.64	0.20
Heritabilities
\({h}^{2}(trait1)\)	0.11	0.11	0.03	0.13	0.02	0.12	0.03	0.12	0.03
\({h}^{2}(trait2)\)	0.50	0.50	0.03	0.50	0.03	0.54	0.03	0.53	0.03
Additive genetic correlations
\({r}_{a}(trait1, trait2)\)	0.30	0.26	0.10	0.24	0.10	0.24	0.10	0.26	0.11
Residual correlations
\({r}_{e}(trait1, trait2)\)	0.10	0.10	0.03	0.10	0.03	0.10	0.03	0.10	0.03

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