@article{Martini2018TheEffect,
 abstract = {BACKGROUND

The single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text]. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text], which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text]. Since the definition of this blending is based on the equation describing [Formula: see text], its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text].

RESULTS

Here, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set.

CONCLUSION

Our results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text].},
 author = {Martini, Johannes W. R. and Schrauf, Matias F. and Garcia-Baccino, Carolina A. and Pimentel, Eduardo C. G. and {[...]} and Simianer, Henner},
 year = {2018},
 title = {The effect of the H\textsuperscript{-1} scaling factors \textgreek{t} and \textgreek{w} on the structure of H in the single-step procedure},
 keywords = {gen;phd},
 pages = {16},
 volume = {50},
 number = {1},
 journal = {Genetics, Selection, Evolution : GSE},
 doi = {10.1186/s12711-018-0386-x},
 file = {http://www.ncbi.nlm.nih.gov/pubmed/29653506},
 file = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5899415},
 howpublished = {refereed}
}

{"_id":"CJfcJK8wLqx7z2Svv","bibbaseid":"martini-schrauf-garciabaccino-pimentel--simianer-theeffectofthehtextsuperscript1scalingfactorstextgreektandtextgreekwonthestructureofhinthesinglestepprocedure-2018","authorIDs":[],"author_short":["Martini, J. W. R.","Schrauf, M. F.","Garcia-Baccino, C. A.","Pimentel, E. C. G.","[...]","Simianer, H."],"bibdata":{"bibtype":"article","type":"article","abstract":"BACKGROUND The single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text]. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text], which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text]. Since the definition of this blending is based on the equation describing [Formula: see text], its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text]. RESULTS Here, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set. CONCLUSION Our results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text].","author":[{"propositions":[],"lastnames":["Martini"],"firstnames":["Johannes","W.","R."],"suffixes":[]},{"propositions":[],"lastnames":["Schrauf"],"firstnames":["Matias","F."],"suffixes":[]},{"propositions":[],"lastnames":["Garcia-Baccino"],"firstnames":["Carolina","A."],"suffixes":[]},{"propositions":[],"lastnames":["Pimentel"],"firstnames":["Eduardo","C.","G."],"suffixes":[]},{"firstnames":[],"propositions":[],"lastnames":["[...]"],"suffixes":[]},{"propositions":[],"lastnames":["Simianer"],"firstnames":["Henner"],"suffixes":[]}],"year":"2018","title":"The effect of the H\\textsuperscript-1 scaling factors \\textgreekt and \\textgreekw on the structure of H in the single-step procedure","keywords":"gen;phd","pages":"16","volume":"50","number":"1","journal":"Genetics, Selection, Evolution : GSE","doi":"10.1186/s12711-018-0386-x","file":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5899415","howpublished":"refereed","bibtex":"@article{Martini2018TheEffect,\r\n abstract = {BACKGROUND\r\n\r\nThe single-step covariance matrix H combines the pedigree-based relationship matrix [Formula: see text] with the more accurate information on realized relatedness of genotyped individuals represented by the genomic relationship matrix [Formula: see text]. In particular, to improve convergence behavior of iterative approaches and to reduce inflation, two weights [Formula: see text] and [Formula: see text] have been introduced in the definition of [Formula: see text], which blend the inverse of a part of [Formula: see text] with the inverse of [Formula: see text]. Since the definition of this blending is based on the equation describing [Formula: see text], its impact on the structure of [Formula: see text] is not obvious. In a joint discussion, we considered the question of the shape of [Formula: see text] for non-trivial [Formula: see text] and [Formula: see text].\r\n\r\nRESULTS\r\n\r\nHere, we present the general matrix [Formula: see text] as a function of these parameters and discuss its structure and properties. Moreover, we screen for optimal values of [Formula: see text] and [Formula: see text] with respect to predictive ability, inflation and iterations up to convergence on a well investigated, publicly available wheat data set.\r\n\r\nCONCLUSION\r\n\r\nOur results may help the reader to develop a better understanding for the effects of changes of [Formula: see text] and [Formula: see text] on the covariance model. In particular, we give theoretical arguments that as a general tendency, inflation will be reduced by increasing [Formula: see text] or by decreasing [Formula: see text].},\r\n author = {Martini, Johannes W. R. and Schrauf, Matias F. and Garcia-Baccino, Carolina A. and Pimentel, Eduardo C. G. and {[...]} and Simianer, Henner},\r\n year = {2018},\r\n title = {The effect of the H\\textsuperscript{-1} scaling factors \\textgreek{t} and \\textgreek{w} on the structure of H in the single-step procedure},\r\n keywords = {gen;phd},\r\n pages = {16},\r\n volume = {50},\r\n number = {1},\r\n journal = {Genetics, Selection, Evolution : GSE},\r\n doi = {10.1186/s12711-018-0386-x},\r\n file = {http://www.ncbi.nlm.nih.gov/pubmed/29653506},\r\n file = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5899415},\r\n howpublished = {refereed}\r\n}\r\n\r\n\r\n","author_short":["Martini, J. W. R.","Schrauf, M. F.","Garcia-Baccino, C. A.","Pimentel, E. C. G.","[...]","Simianer, H."],"key":"Martini2018TheEffect","id":"Martini2018TheEffect","bibbaseid":"martini-schrauf-garciabaccino-pimentel--simianer-theeffectofthehtextsuperscript1scalingfactorstextgreektandtextgreekwonthestructureofhinthesinglestepprocedure-2018","role":"author","urls":{},"keyword":["gen;phd"],"metadata":{"authorlinks":{}},"downloads":0},"bibtype":"article","biburl":"http://www.uni-goettingen.de/de/document/download/9d7c40531010bf5be953ccd9446e47ae.bib/GRK1644BibHomepage.bib","creationDate":"2020-12-14T16:55:09.325Z","downloads":0,"keywords":["gen;phd"],"search_terms":["effect","textsuperscript","scaling","factors","textgreekt","textgreekw","structure","single","step","procedure","martini","schrauf","garcia-baccino","pimentel","[...]","simianer"],"title":"The effect of the H\\textsuperscript-1 scaling factors \\textgreekt and \\textgreekw on the structure of H in the single-step procedure","year":2018,"dataSources":["psxr4mFyE5JDwFLuZ","2w3D54bmLuhpt4TNv","t8S6Y6RWEwDAQHiSQ","cLGdYAfLyvQDgrYmh"]}