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Confidence Intervals On Ratios Of Variance Components In The Three Stage Nested Unbalanced Model
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Book Synopsis Confidence Intervals on Ratios of Variance Components in the Three Stage Nested Unbalanced Model by : Bhabesh Sen
Download or read book Confidence Intervals on Ratios of Variance Components in the Three Stage Nested Unbalanced Model written by Bhabesh Sen and published by . This book was released on 1988 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Confidence Intervals on Variance Components by : Burdick
Download or read book Confidence Intervals on Variance Components written by Burdick and published by CRC Press. This book was released on 1992-02-28 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summarizes information scattered in the technical literature on a subject too new to be included in most textbooks, but which is of interest to statisticians, and those who use statistics in science and education, at an advanced undergraduate or higher level. Overviews recent research on constructin
Book Synopsis Analysis of Variance for Random Models, Volume 2: Unbalanced Data by : Hardeo Sahai
Download or read book Analysis of Variance for Random Models, Volume 2: Unbalanced Data written by Hardeo Sahai and published by Springer Science & Business Media. This book was released on 2007-07-03 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs with a detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level. It also includes numerical examples to analyze data from a wide variety of disciplines as well as any worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example.
Book Synopsis Confidence Intervals for Variance Components by : Kathleen G. Purdy
Download or read book Confidence Intervals for Variance Components written by Kathleen G. Purdy and published by . This book was released on 1998 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measuring the source and magnitude of components of variation has important applications in industrial, environmental and biological studies. This thesis considers the problem of constructing confidence intervals for variance components in Gaussian mixed linear models. A number of methods based on the usual ANOVA mean squares have been proposed for constructing confidence intervals for variance components in balanced mixed models. Some authors have suggested extending balanced model procedures to unbalanced models by replacing the ANOVA mean squares with mean squares from an unweighted means ANOVA. However, the unweighted means ANOVA is only defined for a few specific mixed models. In Chapter 2 we define a generalization of the unweighted means ANOVA for the three variance component mixed linear model and illustrate how the mean squares from this ANOVA may be used to construct confidence intervals for variance components. Computer simulations indicate that the proposed procedure gives intervals that are generally consistent with the stated confidence level, except in the case of extremely unbalanced designs. A set of statistics that can be used as an alternative to the generalized unweighted mean squares is developed in Chapter 3. The intervals constructed with these statistics have better coverage probability and are often narrower than the intervals constructed with the generalized unweighted mean squares.
Book Synopsis Analysis of Variance for Random Models by : Hardeo Sahai
Download or read book Analysis of Variance for Random Models written by Hardeo Sahai and published by Springer Science & Business Media. This book was released on 2004-05-27 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences. This two-volume work is a comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. Volume I examines models with balanced data (orthogonal models); Volume II studies models with unbalanced data (nonorthogonal models). Features and Topics: * Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs * Detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level * Numerical examples to analyze data from a wide variety of disciplines * Many worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example * Extensive exercise sets at the end of each chapter * Numerous appendices with background reference concepts, terms, and results * Balanced coverage of theory, methods, and practical applications * Complete citations of important and related works at the end of each chapter, as well as an extensive general bibliography Accessible to readers with only a modest mathematical and statistical background, the work will appeal to a broad audience of students, researchers, and practitioners in the mathematical, life, social, and engineering sciences. It may be used as a textbook in upper-level undergraduate and graduate courses, or as a reference for readers interested in the use of random effects models for data analysis.
Book Synopsis Confidence Intervals for Variance Components in Unbalanced Models by : Rana S. Fayyad
Download or read book Confidence Intervals for Variance Components in Unbalanced Models written by Rana S. Fayyad and published by . This book was released on 1995 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Analysis of Variance by : Hardeo Sahai
Download or read book The Analysis of Variance written by Hardeo Sahai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of variance (ANOYA) models have become one of the most widely used tools of modern statistics for analyzing multifactor data. The ANOYA models provide versatile statistical tools for studying the relationship between a dependent variable and one or more independent variables. The ANOYA mod els are employed to determine whether different variables interact and which factors or factor combinations are most important. They are appealing because they provide a conceptually simple technique for investigating statistical rela tionships among different independent variables known as factors. Currently there are several texts and monographs available on the sub ject. However, some of them such as those of Scheffe (1959) and Fisher and McDonald (1978), are written for mathematically advanced readers, requiring a good background in calculus, matrix algebra, and statistical theory; whereas others such as Guenther (1964), Huitson (1971), and Dunn and Clark (1987), although they assume only a background in elementary algebra and statistics, treat the subject somewhat scantily and provide only a superficial discussion of the random and mixed effects analysis of variance.
Book Synopsis Confidence Intervals on a Ratio of Variances in the Two-Factor Nested Components of Variance Model by : Franklin A. Graybill
Download or read book Confidence Intervals on a Ratio of Variances in the Two-Factor Nested Components of Variance Model written by Franklin A. Graybill and published by . This book was released on 1980 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider the two-factor nested components of variance model Y sub ijk = mu + A sub i + B sub ij + C sub ijk, where Var(A sub i) = sigma squared sub A Var(B sub ij) = sigma-squared sub B, Var(C sub ijk) = sigma-squared sub C. Confidence intervals are derived for sigma-squared sub A/sigma-squared sub C, sigma-squared sub A (sigma-squared sub A + sigma-squared sub C) and sigma-squared sub C/(sigma-squared sub A + sigma-squared sub C). (Author).
Book Synopsis Confidence Intervals on Functions of Variance Components in Unbalanced Two-way Design Models by : Syamala Srinivasan
Download or read book Confidence Intervals on Functions of Variance Components in Unbalanced Two-way Design Models written by Syamala Srinivasan and published by . This book was released on 1986 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Confidence Intervals on Several Functions of the Components of Variance in a One-way Random Effects Experiment by : Aleksandra Anna Banasik
Download or read book Confidence Intervals on Several Functions of the Components of Variance in a One-way Random Effects Experiment written by Aleksandra Anna Banasik and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Variability is inherent in most data and often it is useful to study the variability so scientists are able to make more accurate statements about their data. One of the most popular ways of analyzing variance in data is by making use of a one-way ANOVA which consists of partitioning the variability among observations into components of variability corresponding to between groups and within groups. One then has [Theta](subY)(superscript 2)=[Theta] (sub A) (superscript)2+[Theta](sub e)(superscript 2). Thus there are two variance components. In certain situations, in addition to estimating these components of variance, it is important to estimate functions of the variance components. This report is devoted to methods for constructing confidence intervals for three particular functions of variance components in the unbalanced One- way random effects models. In order to compare the performance of the methods, simulations were conducted using SAS® and the results were compared across several scenarios based on the number of groups, the number of observations within each group, and the value of sigma (sub A)(superscript 2).
Book Synopsis Variance Components by : Poduri S.R.S. Rao
Download or read book Variance Components written by Poduri S.R.S. Rao and published by CRC Press. This book was released on 1997-06-01 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variance Components Estimation deals with the evaluation of the variation between observable data or classes of data. This is an up-to-date, comprehensive work that is both theoretical and applied. Topics include ML and REML methods of estimation; Steepest-Acent, Newton-Raphson, scoring, and EM algorithms; MINQUE and MIVQUE, confidence intervals for variance components and their ratios; Bayesian approaches and hierarchical models; mixed models for longitudinal data; repeated measures and multivariate observations; as well as non-linear and generalized linear models with random effects.
Book Synopsis Confidence Regions for Variance Components in Unbalanced Mixed Linear Models by : Alan P. Fenech
Download or read book Confidence Regions for Variance Components in Unbalanced Mixed Linear Models written by Alan P. Fenech and published by . This book was released on 1986 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document presents a general procedure for obtaining exact confidence regions for the variance components in unbalanced mixed linear models. The procedure utilizes, as pivotal quantities, quadratic forms that may depend on the variance components in a complicated way and that are distributed independently as chi-square variates. In the special case of balanced classificatory models, the pivotal quantities simplify to scalar multiples of sums of squares from the usual analysis of variance. The procedure can be easily modified so as to obtain an exact confidence region for ratios of variance components and can be regarded as a generalization of Wald's procedure for obtaining a confidence interval for a single variance ratio. (Author).
Book Synopsis Approximate Confidence Intervals for the Main Effects in an Unbalanced, Mixed Model by : Bengt Berlin
Download or read book Approximate Confidence Intervals for the Main Effects in an Unbalanced, Mixed Model written by Bengt Berlin and published by . This book was released on 1974 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Confidence Intervals on Ratios of Variance Components by : Nancy J. Birch
Download or read book Confidence Intervals on Ratios of Variance Components written by Nancy J. Birch and published by . This book was released on 1988 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Confidence Intervals for Proportions of Variability in Two-Factor Nested Variance Component Models by : Franklin A. Graybill
Download or read book Confidence Intervals for Proportions of Variability in Two-Factor Nested Variance Component Models written by Franklin A. Graybill and published by . This book was released on 1977 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Confidence Intervals for Functions of Variance Components by : Kok-Leong Chiang
Download or read book Confidence Intervals for Functions of Variance Components written by Kok-Leong Chiang and published by . This book was released on 2000 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moreover, it is extremely easy to implement and delivers both "equal-tail" and "shortest-length" confidence intervals for any parametric function of interest. (In contrast, only a small number of MLS methods have prescriptions for computing a sort of "shortest-length" interval.) We demonstrate the effectiveness of the proposed method for estimating several commonly studied functions of variance components in various standard models, including the two-way random effects model (with and without interaction), the two-fold nested random effects model and the three-factor cross-classification random effects model. We show that the proposed intervals easily maintain the nominal confidence level and have average interval lengths that are comparable to or better than those of the best existing methods. Moreover, we show that in a particular application, the standard MLS method of Gui et al. (1995) can be extremely liberal, while the proposed method easily maintains the nominal confidence level.
Book Synopsis Statistical Tests for Mixed Linear Models by : André I. Khuri
Download or read book Statistical Tests for Mixed Linear Models written by André I. Khuri and published by John Wiley & Sons. This book was released on 2011-09-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced discussion of linear models with mixed or randomeffects. In recent years a breakthrough has occurred in our ability todraw inferences from exact and optimum tests of variance componentmodels, generating much research activity that relies on linearmodels with mixed and random effects. This volume covers the mostimportant research of the past decade as well as the latestdevelopments in hypothesis testing. It compiles all currentlyavailable results in the area of exact and optimum tests forvariance component models and offers the only comprehensivetreatment for these models at an advanced level. Statistical Tests for Mixed Linear Models: Combines analysis and testing in one self-containedvolume. Describes analysis of variance (ANOVA) procedures in balancedand unbalanced data situations. Examines methods for determining the effect of imbalance ondata analysis. Explains exact and optimum tests and methods for theirderivation. Summarizes test procedures for multivariate mixed and randommodels. Enables novice readers to skip the derivations and discussionson optimum tests. Offers plentiful examples and exercises, manyof which are numerical in flavor. Provides solutions to selected exercises. Statistical Tests for Mixed Linear Models is an accessiblereference for researchers in analysis of variance, experimentaldesign, variance component analysis, and linear mixed models. It isalso an important text for graduate students interested in mixedmodels.
