Effect of missing values in multi‐environmental trials on variance component estimates

Abstract

AbstractA common task in the analysis of multi‐environmental trials (MET) by linear mixed models (LMM) is the estimation of variance components (VCs). Most often, MET data are imbalanced (e.g., due to selection). The imbalance mechanism can be missing completely at random (MCAR), missing at random (MAR), or missing not at random. If the missing‐data pattern in MET was caused by selection, it is usually MAR. In this case, likelihood‐based methods are the preferred methods for analysis as they can account for a MAR data pattern. Likelihood‐based methods used to estimate VCs in LMM have the property that all VC estimates are constrained to be non‐negative; thus, the estimators are generally biased. Therefore, there are two potential causes of bias in MET analysis: a data pattern not being MCAR, and the bias of likelihood‐based VC estimators. The current study tries to dissect and quantify both possible sources of bias. A simulation study with MET data typical of cultivar evaluation trials was conducted in which the missing data pattern and the size of VCs were varied. The results showed that for the simulated MET, bias in VC estimates was similar under MCAR and MAR. Thus, the bias is solely due to the likelihood‐based estimation. Bias increases when increasing the ratio of genotype variance to error variance is small. Bias was similar for MAR and MCAR data patterns. Thus, it may be concluded that selection does not increase bias in VC estimation.