2015
DOI: 10.1007/s00362-015-0706-y
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On a mixed model analysis of multi-environment variety trials: a reconsideration of the one-stage and the two-stage models and analyses

Abstract: This article has been published with an erroneous version of Eq. 15. Please find the correct Eq. 15 in this document. Derivation of (11) Let T = [T 1 T 2 ] be an (n 9 n) non-singular transformation matrix such that T 1 and T 2 , of dimension (n 9 t) and (n 9 (n-t)), satisfy T T 1 X ¼ I t T T 2 X ¼ 0 , RðT 2 Þ ? RðXÞ: Likewise, let Q = [Q 1 Q 2 ] be an ((n-t) 9 (n-t)) non-singular transformation matrix such that Q 1 and Q 2 , of dimension ((n-t) 9 d) and ((n-t) 9 (n-t-d)), satisfy Q T 1 T T 2 X g ¼ I d Q T 2 T … Show more

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Cited by 11 publications
(14 citation statements)
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“…Additionally, the analysis of general combining ability (GCA) for seed yield of Ogura CMS lines and semi-RS DH lines was carried out. The data from all three experiments were processed using the computer program SERGEN [17] based on the methods developed by Kaczmarek [18] and Caliński et al [19, 20, 21]. Heterosis of hybrids between Ogura CMS lines and semi-RS DH lines with the Rfo gene was calculated in respect of the mean seed yield value of both parents and the mean of the better parent.…”
Section: Methodsmentioning
confidence: 99%
“…Additionally, the analysis of general combining ability (GCA) for seed yield of Ogura CMS lines and semi-RS DH lines was carried out. The data from all three experiments were processed using the computer program SERGEN [17] based on the methods developed by Kaczmarek [18] and Caliński et al [19, 20, 21]. Heterosis of hybrids between Ogura CMS lines and semi-RS DH lines with the Rfo gene was calculated in respect of the mean seed yield value of both parents and the mean of the better parent.…”
Section: Methodsmentioning
confidence: 99%
“…Secondly, data from the six environments were combined and analyzed using SERGEN version 3 software (Caliński et al 1998). This program is based on the Sheffe-Caliński mixed model (Scheffe 1959;Caliński 1966;Mądry and Kang 2005) and the Caliński-Kaczmarek joint regression model (Kaczmarek 1986;Caliński et al 1997;Mądry and Kang 2005).…”
Section: Discussionmentioning
confidence: 99%
“…Usually, the stability of plant traits is assessed in multi-environment trials, which are analysed using either a two-stage or one-stage approach (see e.g. Piepho et al ., 2012; Caliński et al ., 2017; Damesa et al ., 2017; Studnicki et al ., 2019). In the two-stage approach, one first analyses each trial separately and next, variety means are analysed using AMMI models or linear mixed models.…”
Section: Discussionmentioning
confidence: 99%