Showing papers on "Mixed model published in 1969"
TL;DR: In this article, a self-contained analysis of a mixed model for regressions is given, which differs from the ordinary covariance model as well as from the error components regression model considered by Mundlak (1963), Wallace & Hussain (1969) and some other writers.
Abstract: This paper gives a self-contained analysis of a mixed model for regressions. The model differs from the ordinary covariance model as well as from the error components regression model considered by Mundlak (1963), Wallace & Hussain (1969) and some other writers. A single-equation mixed regression model is specified and its connexion with Spj0tvoll's mixed model (1966) for analysis of variance is examined. An efficient two-stage method for estimating the parameters of the single-equation model is also given. The multi-regression mixed model is defined and system estimators for the parameters of the model are derived, which have some optimal asymptotic properties.
9 citations
TL;DR: The results suggest that the analysis of variance models with a block design and heteroscedastic errors between locations are more appropriate than their homogeneous residual variance versions.
Abstract: Multi-Environment Trials (METs) are used to make recommendations about genotypes at many stages of plant breeding programs. Because of the genotype-environment interaction, METs are usually conducted in various environments (locations and/or years), using designs which involve several repetitions (plots) for each genotype at each environment. The stratification or blocking of plots within each environment enables one to consider part of the variability due to differences between plots. The objective of this study was to see how frequently the problem of heterogeneous variances across environments appears in Peanut Breeding Program METs, and to evaluate the effects of diverse spatial modeling strategies on the comparison of genotype means in each environment. A series of 18 METs in a peanut breeding program with randomized complete block design in each environment were simultaneously adjusted by using 1) classic analysis of variance models (fixed and random block effects); 2) mixed models adjusted with homogenous and heterogeneous residual variances to take into account that experiments conducted in different environments may vary in precision (residual variances). The results suggest that the analysis of variance models with a block design and heteroscedastic errors between locations are more appropriate than their homogeneous residual variance versions.
5 citations
5 citations
TL;DR: The use of vectors and vector spaces for the representation of the fixed-effects models for the analysis of variance (ANOVA) is well-known as discussed by the authors This representation gives a clear understanding of the estimation and hypothesis testing problems.
Abstract: Summary The use of vectors and vector spaces for the representation of the fixed-effects models for the analysis of variance (ANOVA) is well-known This representation gives a clear understanding of the estimation and hypothesis testing problems
A similar representation can be used for the random-effects models and some mixed models As a result the distribution and the expectation of the mean squares in the ANOVA table can easily be derived
3 citations