Analysis of Variance for Random Models

Sahai, Hardeo; Ojeda, Mario Miguel

doi:10.1007/978-0-8176-8168-5

Cited by 67 publications

(49 citation statements)

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“…And then, dividing the value of σ 2 α whose values fall outside of the confidence interval by the total number of 30 000 trials, type I error rates were found. Since there is a solution only for σ 2 α >0 in terms of ML and REML methods, the negative predicted values of σ 2 α s were assumed to be zero (Sahai & Ojeda 2005):…”

Section: Methodsmentioning

confidence: 99%

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Type I error rates and test power for some variance components estimation methods: one-way random effect model

Mendeş

2012

Arch. Anim. Breed.

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This study was conducted to compare Type I error and test power of ANOVA, REML and ML methods by Monte Carlo simulation technique under different experimental conditions. Simulation results indicated that the variance ratios, sample size and number of groups were important factors in determining appropriate methods which were used to estimate variance components. The ML method was found slightly superior when compared to ANOVA and REML methods. On the other hand, ANOVA and REML methods generated similar results in general. As a results, regardless of distribution shapes and number of groups and if n<15; ML, REML methods might be preferred to the ANOVA. However, when either number of groups or sample size was increased (n≥15) ANOVA method may also be used along with ML and REML.

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Section: Methodsmentioning

confidence: 99%

“…In random-effects model, the expected value and variance of y ij is μ and σ (Thompson 1962, Kelly & Mathew 1993, Rao 2001, Sahai & Ojeda 2004, Searle et al 2006.…”

Section: Methodsmentioning

confidence: 99%

Type I error rates and test power for some variance components estimation methods: one-way random effect model

Mendeş

2012

Arch. Anim. Breed.

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“…The linear model for three-way unbalanced nested arrangement is given by Sahai and Ojeda (2004) as Eq. 1:…”

Section: Statistical Modelmentioning

confidence: 99%

“…Tietjen and Moore (1968) developed a fast procedure for computing approximate F-test in unbalanced nested analysis of variance. Sahai and Ojeda (2004) discussed unbalanced nested analysis of variance for random effect model.…”

Section: Introductionmentioning

confidence: 99%

On Three-Way Unbalance Nested Analysis of Variance

Sanni¹,

Ukaegbu²

2012

Journal of Mathematics and Statistics

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Problem statement: In this study, we give a simple analytically tractable procedure for solving three-way unbalanced nested Analysis of Variance (ANOVA). In many realistic situations, unbalanced design was unavoidable due to natural constraints and missing data. Approach: Here, we present a comprehensive approach for addressing solutions of problems arising from unbalanced nested ANOVA. We consider the F-statistics under the different models. Results: Special attention was given to the construction of approximate F-test where exact F-test does not exist. Pseudo-degrees of freedoms were derived using the Satterthwaite's type approximation. Conclusion: In all derivations, we assume that the effects act independently and that the mean squares are independent. A numerical example is given to illustrate the solution procedure.

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“…In the intercept-only model, the REML estimates are defined by the following system of equations: Sahai and Ojeda, 2005), where MSE = is the estimate of i . Equation (7) …”

Section: The Modelmentioning

confidence: 99%