On a mixed model analysis of multi-environment variety trials: a reconsideration of the one-stage and the two-stage models and analyses

• Published in: Statistical papers (Berlin, Germany) Vol. 58; no. 2; pp. 433 - 465
• Main Authors: Caliński, T., Czajka, S., Kaczmarek, Z., Krajewski, P., Pilarczyk, W., Siatkowski, I., Siatkowski, M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2017; Springer Nature B.V
• Subjects: Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Management; Mathematics and Statistics; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Regular Article; Rye; Statistics; Statistics for Business; Hypothesis testing; Series of experiments; Stage-wise analysis; Estimation; Mixed effects model; 62J10; Analysis of variance; 62K10
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-015-0706-y

Of interest is the analysis of results of a series of experiments conducted at several environments with the same set of plant varieties (called multi-environment variety trials). The most common practice is first to analyze individual trials and then to perform a kind of “synthesis” of the results obtained. This is considered as a two-stage approach to the analysis of the trial data. More recently a combined analysis of the raw plot data from all trials taken simultaneously has been advocated, as a one-stage approach to the analysis. The purpose of this article is to reconsider these two approaches with regard to the underlying models and the analyses based on them. The indicated differences between them are illustrated by a thorough analysis of a set of data from a series of trials with rye varieties. The required computations have been accomplished with the use of R.