Application of supernodal sparse factorization and inversion to the estimation of (co)variance components by residual maximum likelihood

We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left‐looking and inverse multifrontal algorithms...

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Bibliographic Details
Published in:Journal of animal breeding and genetics (1986) Vol. 131; no. 3; pp. 227 - 236
Main Authors: Masuda, Y, Baba, T, Suzuki, M
Format: Journal Article
Language:English
Published: Germany Blackwell Wissenschafts-Verlag 01.06.2014
Blackwell Publishing Ltd
Subjects:
Algorithms
Analysis of Variance
Animal models
Animal reproduction
Animals
Breeding
Cattle
Computational Biology
Computational Biology - methods
computer software
Computing methods
Dairying
equations
Female
Genomics
Likelihood Functions
Male
methods
mixed model equations
residual maximum likelihood
sires
Software
sparse matrix
Statistics as Topic
Statistics as Topic - methods
Time Factors
variance
residual maximum likelihood
sparse matrix
mixed model equations
Computing methods
ISSN:0931-2668, 1439-0388, 1439-0388
Online Access:Get full text
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Summary:We demonstrated that supernodal techniques were more efficient than traditional methods for factorization and inversion of a coefficient matrix of mixed model equations (MME), which are often required in residual maximum likelihood (REML). Supernodal left‐looking and inverse multifrontal algorithms were employed for sparse factorization and inversion, respectively. The approximate minimum degree or multilevel nested dissection was used for ordering. A new computer package, Yet Another MME Solver (yams), was developed and compared with fspak with respect to computing time and size of temporary memory for 13 test matrices. The matrices were produced by fitting animal models to dairy data and by using simulations from sire, sire–maternal grand sire, maternal and dominance models for phenotypic data and animal model for genomic data. The order of matrices ranged from 32 840 to 1 048 872. The yams software factorized and inverted the matrices up to 13 and 10 times faster than fspak, respectively, when an appropriate ordering strategy was applied. The yams package required at most 282 MB and 512 MB of temporary memory for factorization and inversion, respectively. Processing time per iteration in average information REML was reduced, using yams. The yams package is freely available on request by contacting the corresponding author.
Bibliography:http://dx.doi.org/10.1111/jbg.12058
Methods S1 Additional comparisons. Results S1 Factorization and inversion.
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ISSN:0931-2668
1439-0388
1439-0388
DOI:10.1111/jbg.12058