Paulo C. Rodrigues

A comparison between Joint Regression Analysis and the Additive Main and Multiplicative Interaction model: the robustness with increasing amounts of missing data

This paper joins the main properties of joint regression analysis (JRA), a model based on the Finlay-Wilkinson regression to analyse multi-environment trials, and of the additive main effects and multiplicative interaction (AMMI) model. The study compares JRA and AMMI with particular focus on robustness with increasing amounts of randomly selected missing data. The application is made using a data set from a breeding program of durum wheat (Triticum turgidum L., Durum Group) conducted in Portugal. The results of the two models result in similar dominant cultivars (JRA) and winner of mega-environments (AMMI) for the same environments. However, JRA had more stable results with the increase in the incidence rates of missing values.

A comparison between joint regression analysis and the AMMI model: a case study with barley

Joint regression analysis (JRA) and additive main effects and multiplicative interaction (AMMI) models are compared in order to (i) access the ability of describing a genotype by environment interaction effects and (ii) evaluate the agreement between the winners of mega-environments obtained from the AMMI analysis and the genotypes in the upper contour of the JRA. An iterative algorithm is used to obtain the environmental indexes for JRA, and standard multiple comparison procedures are adapted for genotype comparison and selection. This study includes three data sets from a spring barley (Hordeum vulgare L.) breeding programme carried out between 2004 and 2006 in Czech Republic. The results from both techniques are integrated in order to advise plant breeders, farmers and agronomists for better genotype selection and prediction for new years and/or new environments.

Analyzing genotype-by-environment interaction using curvilinear regression

In the context of multi-environment trials, where a series of experiments is conducted across different environmental conditions, the analysis of the structure of genotype-by-environment interaction is an important topic. This paper presents a generalization of the joint regression analysis for the cases where the response (e.g. yield) is not linear across environments and can be written as a second (or higher) order polynomial or another non-linear function. After identifying the common form regression function for all genotypes, we propose a selection procedure based on the adaptation of two tests: (i) a test for parallelism of regression curves; and (ii) a test of coincidence for those regressions. When the hypothesis of parallelism is rejected, subgroups of genotypes where the responses are parallel (or coincident) should be identified. The use of the Scheffe multiple comparison method for regression coefficients in second-order polynomials allows to group the genotypes in two types of groups: one with upward-facing concavity (i.e. potential yield growth), and the other with downward-facing concavity (i.e. the yield approaches saturation). Theoretical results for genotype comparison and genotype selection are illustrated with an example of yield from a non-orthogonal series of experiments with winter rye (Secalecereale L.). We have deleted 10 % of that data at random to show that our meteorology is fully applicable to incomplete data sets, often observed in multi-environment trials.

Binary Operations on Orthogonal Models, Application to Prime Basis Factorials and Fractional Replicates

Commutative Jordan algebras (CJA) are used in the study of orthogonal models either simple or derived through model crossing and model nesting. Once normality is assumed, UMVUE are obtained for relevant parameters.The general treatment is then applied to models obtained from prime basis factorials or their fractional replicates. Besides model crossing and nesting, factor merging is considered. In this way we may extend our results to factors with whatever number of levels instead of factors whose numbers of levels are powers of the same prime.