Reducing computational demands of restricted maximum likelihood estimation with genomic relationship matrices

Table 1 Elapsed times (seconds) for analyses of the simulated data

		Means only					Contemporary groups
	\(t^{\text{a}}\)	1	2	3	4	5	1	2	3	4	5
NEQ^b		21,001	42,002	63,003	84,004	105,005	23,408	46,816	70,224	93,632	117,040
Pedigree relationships only
Setup^c	MV^d	1	3	6	9	13	2	6	12	22	33
	PC^e	1	3	6	9	14	2	6	12	22	33
Iterate^f	MV	< 1	1	2	5	8	1	7	19	39	74
	PC	< 1	1	2	5	9	1	7	19	40	75
Pedigree and genomic relationships
Setup	MV	28	195	636	1459	2,836	30	203	643	1502	2896
	PC	28	71	141	225	321	32	81	154	251	374
Iterate	MV	14	206	1209	4424	12,357	19	243	1282	4637	12,853
	PC	8	34	87	171	292	12	56	134	262	549
	R^g	1.8	6.1	13.9	25.9	42.3	1.6	4.3	9.6	17.7	28.0
NZ-C^h	MV	8.61	34.36	77.27	137.32	214.52	8.61	34.37	77.29	137.35	214.57
	PC	8.61	17.28	26.00	34.80	43.66	8.61	17.29	26.03	34.84	43.71
NZ-Lⁱ	MV	11.77	47.02	105.74	187.93	293.61	21.06	83.98	188.91	335.79	524.63
	PC	11.77	46.98	105.63	187.72	293.25	21.06	83.94	188.78	335.54	524.22

^aNumber of traits considered
^bNumber of equations in mixed model
^cTime for set-up steps of REML analysis
^dStandard multivariate parameterisation
^ePrincipal components parameterisation
^fTime per AI-REML iterate
^gRatio of times per iterate: MV/PC
^hNumber of non-zero elements in one triangle of the coefficient matrix; in millions
ⁱNumber of non-zero elements in the Cholesky factor of the coefficient matrix; in millions

ISSN: 1297-9686