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Some Methods for Analyzing Multi-trait Genotype-by-Environment Interactions
Modeling complex interactions involving multiple response variables is a difficult problem. Response variables are often correlated with each other, have causal relationships and are influenced by factor main effects, interactions and covariates. When analyzing these types of data, the covariance(s) and causal structure among the traits and the random structure due to factor and/or the experimental design should be taken into consideration. Ignoring anyone or more of them, during the analysis process, can limit the scope of the analysis and reduce the inference space. Modeling both causal structure and random structure is difficult and either totally ignored or estimated via Bayesian methods. Use of a classical mixed model framework has been avoided since causal modeling is often considered too complex. We propose a simple modification to the classical causal model that allows using restricted maximum likelihood (REML) to estimate both causal and random structures. We call this model a linear system with random effects (LSRE) and we show it has good statistical properties in that the estimates are consistent and asymptotically normal. ^ The LSRE model is a special form of the multivariate linear mixed model that can be fitted with methods for multivariate linear mixed models using the modified Cholesky decomposition. The proposed model can account for complex covariance structures due to random effects and/or the experimental design and can fit recursive causal structures among the traits simultaneously. This model also allows incorporation of any correlation structure among the observations. This model can be used to produce BLUPs that when used with other methods, e.g. Tucker's three mode decomposition, give increased explanatory power compared to traditional fixed effects methods. Tucker's three mode decomposition breaks down the three-way interaction into a smaller number of multiplicative terms with the presumption that most of the three-way interaction can be explained by the first few meaningful components of each mode. BLUPs shrink towards their means and therefore, the predictors are smoother than means obtained using fixed effects approaches and has additional advantage over the means approaches when data are unbalanced or missing.^ The LSRE model was implemented on simulated data and a real wheat genetics data set. The analysis on simulated data gave results very close to the true parameters. The results obtained from real data set made biological sense and provided a clearer understanding than traditional methods for the analysis of genotype-by-environment interaction in wheat.^
Yaseen, Muhammad, "Some Methods for Analyzing Multi-trait Genotype-by-Environment Interactions" (2012). ETD collection for University of Nebraska - Lincoln. AAI3527706.