Mixed model with spatial variance–covariance structure for accommodating of local stationary trend and its influence on multi-environmental crop variety trial assessment

  • Asnake Worku Negash School of Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Pietermaritzburg
  • Henry Mwambi School of Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Pietermaritzburg
  • Temesgen Zewotir School of Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Pietermaritzburg
  • Girma Aweke CIMMYT, Addis Ababa
Keywords: multi-environmental trials, chi-squared test, spatial variance–covariance, consistency ratio test, wheat, barley


The most common procedure for analyzing multi-environmental trials is based on the assumption that the residual error variance is homogenous across all locations considered. However, this may often be unrealistic, and therefore limit the accuracy of variety evaluation or the reliability of variety recommendations. The objectives of this study were to show the advantages of mixed models with spatial variance–covariance structures, and direct implications of model choice on the inference of varietal performance, ranking and testing based on two multi-environmental data sets from realistic national trials. A model comparison with a chi-square test for the trials in the two data sets (wheat data set BW00RVTI and barley data set BW01RVII) suggested that selected spatial variance-covariance structures fitted the data significantly better than the ANOVA model. The forms of optimally-fitted spatial variance-covariance, ranking and consistency ratio test were not the same from one trial (location) to the other. Linear mixed models with single stage analysis including spatial variance-covariance structure with a group factor of location on the random model also improved the real estimation of genotype effect and their ranking. The model also improved varietal performance estimation because of its capacity to handle additional sources of variation, location and genotype by location (environment) interaction variation and accommodating of local stationary trend.


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Author Biography

Asnake Worku Negash, School of Mathematics, Statistics and Computer Science. University of KwaZulu-Natal, Pietermaritzburg
PhD student


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How to Cite
NegashA. W., MwambiH., ZewotirT., & AwekeG. (2014). Mixed model with spatial variance–covariance structure for accommodating of local stationary trend and its influence on multi-environmental crop variety trial assessment. Spanish Journal of Agricultural Research, 12(1), 195-205. https://doi.org/10.5424/sjar/2014121-4926
Plant breeding, genetics and genetic resources