Modified joint regression analysis for incomplete variety × environment data

Digby, P. G. N.

doi:10.1017/s0021859600086159

Cited by 86 publications

(62 citation statements)

References 6 publications

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“…Therefore, the IAC 15 cultivar perhaps should not be considered as the most promising genotype. The phenotypic expression of all the other genotypes assessed was explained by a concave model (Digby, 1979), and were placed in groups B, C and D (Table 1). That is, all these genotypes showed a simple response pattern for the storage root yield characteristic.…”

Section: Resultsmentioning

confidence: 99%

“…This method is based on non-linear regression analysis and has been developed from the non-linear unisegmented model proposed by Digby (1979) The model by Digby (1979) was an interesting proposal for stability studies based on non-linear regression analysis. However, this method was shown to be unable to assess the genotype response in favorable and unfavorable environments simultaneously.…”

Section: Methodsmentioning

confidence: 99%

“…Furthermore, this methodology permits the choice of the model that best explains the phenotypic performance of the genotypes, whether uni or bisegmented. Rejection of the hypothesis H( i 2 β = i 1 β ) implies the choice of the bi-segmented model, while the acceptance of the hypothesis implies the choice of the uni-segmented model (Digby, 1979). Toler and Burrows (1998) also proposed genotype classification in five different groups, according to the following criteria:…”

Section: Methodsmentioning

confidence: 99%

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Comparison of methods for phenotypic stability analysis of cassava (Manihot esculenta Crantz) genotypes for yield and storage root dry matter content

Kvitschal

Filho

Scapim

et al. 2009

Braz. arch. biol. technol.

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Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Comparison of methods for phenotypic stability analysis of cassava (Manihot esculenta Crantz) genotypes for yield and storage root dry matter content

Kvitschal

Filho

Scapim

et al. 2009

Braz. arch. biol. technol.

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“…O processo termina quando as estimativas sucessivas das somas dos quadrados dos desvios (SQD) são minimizadas, o que implica a sua convergência em valores de magnitude mínima, não mais se modificando dentro de um padrão lógico de precisão. TOLER (1990) propôs testes das hipóteses H(β1i = β2i) e H(β1i = β2i = βi = 1) para enquadrar os genótipos em cinco grupos, a saber: A, B, C, D e E. Assim, quando a hipótese H(β1i = β2i) é aceita, esse modelo se resume ao modelo unissegmentado, proposto por DIGBY (1979), que permitirá enquadrar os genótipos nos grupos B, C ou D. Caso contrário, indicará a existência de dois coeficientes de regressão distintos, e os genótipos se enquadrarão nos grupos bissegmentados A ou E, conforme a significância desses parâ-metros. Os critérios são os seguintes:…”

Section: Methodsunclassified

Modelo de regressão não-linear aplicado ao estudo da estabilidade fenotípica de genótipos de feijão no Estado do Paraná

Rosse¹,

Vencovsky²

2000

Bragantia

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RESUMOO presente trabalho teve por objetivo estudar a estabilidade fenotípica da produtividade de grãos de feijão (Phaseolus vulgaris L.) com dados obtidos no Ensaio Regional Final do Estado do Paraná, durante o ano/safra 1996/97, através de modelo não-linear, (nos parâmetros propostos por Toler), assim expresso: Yij = αi + [Zjβ1i + (1 -Zj) β2i] µj + εij. Esse autor propôs testes das hipóteses H(β1i = β2i) e H(β1i = β2i = βi = 1), as quais permitem enquadrar os genótipos em cinco grupos, conforme o padrão de resposta, a saber: A, B, C, D e E. Os parâmetros do modelo são estimados conjuntamente através de quadrados mínimos iterativos (não-lineares), empregando-se neste estudo o método de GaussNewton modificado. Concluiu-se que o modelo foi útil para classificar os materiais genéticos segundo suas produtividades e seus padrões de resposta, o que contribuiu para um maior discernimento de seus comportamentos. As médias dos genótipos dos grupos A e E mostraram-se influenciadas pela associação negativa entre β 1i e β 2i . A maioria dos genótipos com padrão de resposta duplamente favorável (grupo A, padrão convexo) apresentou produtividades baixas. Os genótipos com produtividades mais elevadas enquadraram-se preferencialmente no grupo E (padrão côncavo, duplamente desfavorável). Os genótipos dos grupos com padrão unissegmentado (B, C e D) tiveram produtividades variáveis. Ficou evidenciada a dificuldade em encontrar genótipos associando altas produtividades com padrão de resposta convexo. Palavras-chave: Estabilidade fenotípica, padrão de resposta, feijão. ABSTRACT NON-LINEAR MODEL REGRESSION FOR PHENOTYPIC STABILITY ANALYSIS OF BEAN GENOTYPES IN THE STATE OF PARANÁA phenotypic stability analysis of common bean (Phaseolus vulgaris L.) grain yield (kg.ha -1 ) was carried out using data of the Regional Trial of the State of Paraná during the year/harvest 1996/97. A non-linear model using the parameters proposed by Toler, Yij = αi + [Zjβ1i + (1 -Zj) β2i] µj + εij, was adopted. The author proposed tests of the hypotheses H(β1i = β2i) and H(β1i = β2i = βi = 1) according to the principles of regression analysis, that allow the genotypes to be placed in five groups (A, B, C, D, and E) based on their response pattern. The parameters of the model are simultaneously estimated using iterative (non-linear) least squares through the modified Gauss-Newton method. The model was useful in classifying the genetic materials according to their yield and response patterns, contributing to a greater understanding of their yield behavior. The mean of the A and E groups was influenced by a negative association between β1i and β2i. The majority of genotypes with a double favorable response pattern (A group, convex pattern) had lower yields. Genotypes with higher yields were placed mostly ( 1 ) Recebido para a publicação em 28 de junho e aceito em 22 de novembro de 1999.

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“…The environmental indexes adjusted in this way are called L 2 environmental indexes, because the L 2 norm was used. The described zigzag algorithm is a version of the iterative algorithms existing in the literature; see for example, Digby (1979); Gabriel and Zamir (1979) and Ng and Williams (2001). Pereira and Mexia (2010) proved the convergence of the zigzag algorithm and that the adjusted parameters could be seen as maximum likelihood estimators.…”

Section: The Zigzag Algorithmmentioning

confidence: 99%

Analyzing genotype-by-environment interaction using curvilinear regression

Pereira

Rodrigues

Mejza

et al. 2012

Sci. agric. (Piracicaba, Braz.)

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In the context of multi-environment trials, where a series of experiments is conducted across different environmental conditions, the analysis of the structure of genotype-byenvironment interaction is an important topic. This paper presents a generalization of the joint regression analysis for the cases where the response (e.g. yield) is not linear across environments and can be written as a second (or higher) order polynomial or another non-linear function. After identifying the common form regression function for all genotypes, we propose a selection procedure based on the adaptation of two tests: (i) a test for parallelism of regression curves; and (ii) a test of coincidence for those regressions. When the hypothesis of parallelism is rejected, subgroups of genotypes where the responses are parallel (or coincident) should be identified.The use of the Scheffé multiple comparison method for regression coefficients in second-order polynomials allows to group the genotypes in two types of groups: one with upward-facing concavity (i.e. potential yield growth), and the other with downward-facing concavity (i.e. the yield approaches saturation). Theoretical results for genotype comparison and genotype selection are illustrated with an example of yield from a non-orthogonal series of experiments with winter rye (Secalecereale L.). We have deleted 10 % of that data at random to show that our meteorology is fully applicable to incomplete data sets, often observed in multi-environment trials.

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Modified joint regression analysis for incomplete variety × environment data

Cited by 86 publications

References 6 publications

Comparison of methods for phenotypic stability analysis of cassava (Manihot esculenta Crantz) genotypes for yield and storage root dry matter content

Comparison of methods for phenotypic stability analysis of cassava (Manihot esculenta Crantz) genotypes for yield and storage root dry matter content

Modelo de regressão não-linear aplicado ao estudo da estabilidade fenotípica de genótipos de feijão no Estado do Paraná

Analyzing genotype-by-environment interaction using curvilinear regression

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