We propose a new methodology for multiple imputation when faced with missing data in multi-environmental trials with genotype-by-environment interaction, based on the imputation system developed by Krzanowski that uses the singular value decomposition (SVD) of a matrix. Several different iterative variants are described; differential weights can also be included in each variant to represent the influence of different components of SVD in the imputation process. The methods are compared through a simulation study based on three
real data matrices that have values deleted randomly at different percentages, using as measure of overall accuracy a combination of the variance between imputations and their mean square deviations relative to the deleted values. The best results are shown by two of the iterative schemes that use weights belonging to the interval [0.75, 1]. These schemes provide imputations that have higher quality when compared with other multiple imputation methods based on the Krzanowski method.
Authors: Glenn Healey
Comments: 7 Pages.
Given information about batted balls for a set of players, we review techniques for estimating the reliability of a statistic as a function of the sample size. We also review methods for using the estimated reliability to compute the variance of true talent and to generate forecasts.
One of the main objectives of statistics is to estimate the parameters of a probability distribution based on a sample taken from this distribution.
In multi-environment trials it is common to measure several response variables or attributes to determine the genotypes with the best characteristics. Thus it is important to have techniques to analyse multivariate multi-environment trial data. The main objective is to complement the literature on two multivariate techniques, the mixture maximum likelihood method of clustering and three-mode principal component analysis, used to analyse genotypes, environments and attributes simultaneously. In this way, both global and detailed statements about the performance of the genotypes can be made, highlighting the benefit of using three-way data in a direct way and providing an alternative analysis for researchers. We illustrate using sunflower data with twenty genotypes, eight environments and three attributes. The procedures provide an analytical procedure which is relatively easy to apply and interpret in order to describe the patterns of performance and associations in multivariate multi-environment trials.
Authors: Florentin Smarandache
Comments: 3 Pages.
As in nature nothing is absolute, evidently there will not exist a precise border between the scientific language and “the literary” one (the language used in literature): thus there will be zones where these two languages intersect.