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

Table 2 Elapsed times (seconds) together with the characteristics of the coefficient matrix in the mixed model equations for analyses of sheep data

		Simple animal model				Fitting maternal effects
	t^a	1	2	3	4	1	2	3	4
NP^b		2	6	12	20	4	12	24	40
NEQ^c		112,533	226,368	338,955	447,630	239,309	482,364	723,606	960,498
Pedigree relationships only
Setup^d	MV^e	14	33	57	77	28	88	176	255
	PC^f	14	34	65	100	28	95	206	358
Iterate^g	MV	6	17	31	46	13	47	100	171
	PC	6	17	31	45	13	46	97	176
Pedigree and genomic relationships
Setup	MV	107	660	2093	4860	223	1290	4140	9158
	PC	107	587	1784	3996	223	1137	3298	7126
Iterate	MV	52	644	3620	13,250	157	1783	9965	35,298
	PC	33	121	278	497	109	405	940	1905
	R^h	1.6	5.4	13.0	26.7	1.4	4.4	10.6	18.5
NZ-Cⁱ	MV	19.2	76.4	171.6	304.5	38.6	153.6	344.7	610.6
	PC	19.2	38.6	58.0	77.1	38.6	77.9	117.5	155.9
NZ-L^j	MV	29.2	109.2	249.0	437.5	86.2	346.9	781.3	1343.6
	PC	29.2	111.6	249.8	421.3	86.2	345.5	747.5	1290.4

^aNumber of traits considered
^bNumber of parameters to be estimated
^cNumber of equations in mixed model
^dTime for set-up steps of REML analysis
^eStandard multivariate parameterisation
^fPrincipal components parameterisation
^gTime per AI-REML iterate
^hRatio of times per iterate: MV/PC
ⁱNumber of non-zero elements in one triangle of the coefficient matrix; in millions
^jNumber of non-zero elements in the Cholesky factor of the coefficient matrix; in millions

ISSN: 1297-9686