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Stability analysis based on a bi-segmented discontinuous model with measurement errors in the variables^*

Lindolfo Storck^I; Roland Vencovsky^II

^IDepartamento de Fitotecnia, Universidade Federal de Santa Maria, 97 119-900 Santa Maria, RS, Brasil. Send correspondence to L.S.
^IIDepartamento de Genética, ESALQ-USPUSP, 13418-260 Piracicaba, SP, Brasil

ABSTRACT

A bi-segmented discontinuous model is proposed for stability analysis of genetic materials. The model is defined as: m_ij = b0_i + b1_it_j + b2_itjZ_j + b3_iZ_j + d_ij, such that: t_j is the effect of environment j; Z_j =1 if t_j > 0 and Z_j = 0 if t_j < 0; b1_i; and b1_i + b2_i are the slopes of the two segments; b3_i is the discontinuity parameter for cultivar i; and d_ij is the deviation from the model. This model allowed the determination and measurement of components of variance and covariance of the errors inherent to the independent and dependent variables. A correction was consequently derived for estimation of parameters and tests of hypotheses.

Keywords: stability analysis; bi-segmented discontinuous; measurement errors.

REFERENCES

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* Part of a thesis presented by L.S. to Departarnento de Matemática e Estatística, ESALQ/USP, in partial fulfillment of the requirements for the Doctoral degree.