Effect of Missing Values on Variance Component Estimates in Multienvironment Trials

Abstract

Multienvironment trials (METs) are conducted to evaluate cultivars across locations and years with often incomplete data structure due to annual cultivar replacements. The imbalance could cause biased variance component (VC) estimates depending on data dimension, proportion of missing values, and the cultivar dropout mechanism. The objective of this study was to quantify the bias of VC estimates obtained from imbalanced datasets. We performed simulations of METs with different data dimensions (number of cultivars, locations, and years) using VC parameters taken from real wheat (Triticum aestivum L.) METs. The missing values were generated by annually dropping and replacing cultivars. The genotypic variance estimates obtained from analyses of 2 yr of METs, and >40% missing values, were overestimated in all simulated scenarios. The percentage of bias was highly influenced by the number of years considered for analysis. Variance component estimates from simulations with more years of METs were less biased: 8‐yr analyses produced <5% bias in the genotypic variance and its interactions, even in highly imbalanced datasets. Increasing the number of annually tested cultivars or the number of locations was less beneficial in terms of decreasing bias than increasing the number of years. Cultivar‐mean repeatability was considerably affected by increases in the percentage of missing values, which caused reductions of up to 60% with few years of METs. Results showed that, even with cultivar replacement, linear mixed models can estimate VCs with <5% bias when there are four or more years of METs, with or without imbalance (up to 40%).

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

“…The current simulation as well as the simulation presented in Aguate et al (2019) variances for all random terms and the error. Note that the data were not re-analysed for the current study and therefore VCs were directly taken from Aguate et al (2019).…”

“…Note that the current simulation with BLUP-based selection matches Scenario 1 in Aguate et al (2019) as this scenario showed largest effects on relative bias and root mean square error (RMSE). The authors used four scenarios with the same type of imbalance but increased the size of the data by adding more genotypes and/or more locations compared to Scenario 1.…”

“…The missing data mechanism of BLUP-based selection is MAR (Aguate et al, 2019), as the selection decision was based on observed data only. Note that genotypes in the current study were numbered chronologically in ascending order.…”

“…where is one of the four evaluation criteria in simulation run m mentioned above, is the mean of the corresponding evaluation criterion and is the error of . Here, is the mean squared error ( and the relative bias ( ̂ ), computed as the means of and , respectively (Aguate et al, 2019). Finally, the square root of was calculated and denoted as root mean squared error ( ) of the corresponding q th VC.…”

“…As mixed models are commonly fitted with REML, a MAR data pattern can be ignored for this type of analysis. Further note that linear mixed models are efficient when the drop-out mechanism is MCAR (Aguate et al, 2019) and a complete case analysis is reasonable (Carpenter and Kenward, 2007), though not usually the most efficient option for MET.…”