scholarly journals Optimal Designs For the Restricted Maximum Likelihood Estimators in a Random Split-Plot Model

2017 ◽  
Vol 56 (1) ◽  
pp. 64-71
Author(s):  
Oluwole Nuga ◽  
G. N. Amahia ◽  
Fatai Salami
Keyword(s):  
Maximum Likelihood ◽  
Variance Components ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Restricted Maximum Likelihood ◽  
Optimal Designs ◽  
Absolute Difference ◽  
Statistical Efficiency ◽  
Split Plot ◽  
True Values

The design effect for the restricted maximum likelihood estimators of variance components in acompletely randomized split-plot model is studied. The model was used to represent the response generated froman experimental scenario where the whole-plot and split-plot factors are random. The work generated groups ofbalanced designs from same number of experimental runs and compared them for optimality using the derived Fisher Information matrix of the restricted maximum likelihood (REML) estimators. The measure for optimalityis the D-optimality criterion; the resulting optimal designs depend on the relative magnitudes of the true values of the variance components. The results show that when the factor variances are larger than the error variances, designs where the absolute difference between the number of whole-plots and the number of levels of the splitplot factor is relatively small show substantial gain in statistical efficiency over other designs.

Animal x testing environment interaction on postweaning liveweight gains of young bulls

1998 ◽  
Vol 49 (4) ◽  
pp. 607 ◽  
Author(s):  
S. J. Schoeman ◽  
G. G. Jordaan
Keyword(s):  
Maximum Likelihood ◽  
Genetic Correlation ◽  
Variance Components ◽  
Restricted Maximum Likelihood ◽  
Animal Breeding ◽  
Environment Interaction ◽  
Maximum Likelihood Analysis ◽  
Breeding Values ◽  
Testing Environment ◽  
Likelihood Analysis

Postweaning liveweight gain records of 1610 young bulls obtained both in feedlot and under pasture were used to estimate (co)variance components using a multivariate restricted maximum likelihood analysis. The pedigree file included 3477 animals. Heritability estimates for liveweights and gain in both environments correspond to most previously reported estimates. The genetic correlation of gain between the 2 environments was -0·12, suggesting a large genotype testing environment interaction and re-ranking of animal breeding values across environments. Results of this analysis suggest the need for environment-specific breeding values for postweaning gain.

scholarly journals Generalized Truncation Positive Normal Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1361
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Data Sets ◽  
New Model ◽  
Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

An Alternative Method for Estimating Variance Components in Generalizability Theory

1990 ◽  
Vol 66 (2) ◽  
pp. 379-386 ◽  
Author(s):  
George A. Marcoulides
Keyword(s):  
Maximum Likelihood ◽  
Analysis Of Variance ◽  
Variance Components ◽  
Generalizability Theory ◽  
Simulated Data ◽  
Restricted Maximum Likelihood ◽  
Alternative Method ◽  
Sample Data

This study compares, using simulated data, two methods for estimating variance components in generalizability (G) studies. Traditionally variance components are estimated from an analysis of variance of sample data. The alternative method for estimating variance components is restricted maximum likelihood (REML). The results indicate that REML provides estimates for the components in the various designs that are closer to the true parameters than the estimates from analysis of variance.

scholarly journals On estimation in multilevel models with block circular symmetric covariance structure

2012 ◽  
Vol 16 (1) ◽  
pp. 83-96
Author(s):  
Yuli Liang ◽  
Dietrich von Rosen ◽  
Tatjana von Rosen
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Parameter Space ◽  
Variance Components ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Covariance Structure ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

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