| Multi-environment trials are the most basic and widely used agricultural trials. Genotype-by-environment interaction (GE) is a common phenomenon in crops. While, in multi-environment trials, missing values often occur because of various reasons. In this dissertation, we study analysis method for genotype-by-environment interaction effect in the presence of missing data.Since Additive Main effects and Multiplicative Interaction (AMMI) model, Geno-type main effect plus Genotype-Environment interaction (GGE) model and joint re-gression model (F-W model) are commonly used in GE effect analysis, this dissertation considers these three models. In this dissertation, it is considered that whether effects of genotype and/or environment are regarded as random variables are considered. Firstly, the effects of genotype and environment are set as fixed effects, namely for fixed effect case, this dissertation presents parameter estimation of AMMI model and GGE model under missing data based on EM algorithm. Secondly, with effects of genotype fixed, and effects of environment being random, we discuss an extension of F-W model to het-eroscedastic mixed model. The maximum likelihood estimation is derived. For there is no closed form to the maximum likelihood estimation, usually iteration methods are used. Meanwhile, because of its good nature EM algorithm is often used in missing data situation. This dissertation also gives the corresponding parameter estimation method based on EM algorithm.Finally, a real trial dataset is used to illustrate the effect of EM parameter esti-mation for GGE model in fixed effect situation. As a result, when the proportion of missing data is not high, after using our method to impute missing values, we can suc-cessfully recover the main pattern of the original data. At the same time, with a missing dataset, our method's impact on general adaptability, special adaptability, environment discrimitiveness and representativeness and so on is investigated. |
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