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UNINA9910143186203321 |
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Autore |
McCulloch Charles E. |
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Titolo |
Generalized, linear, and mixed models / / Charles E. McCulloch, Shayle R. Searle |
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Pubbl/distr/stampa |
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New York, [New York] : , : John Wiley & Sons, Ltd, , 2001 |
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©2001 |
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ISBN |
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1-280-27278-3 |
9786610272785 |
0-470-34244-7 |
0-471-65404-3 |
0-471-72207-3 |
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Descrizione fisica |
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1 online resource (358 p.) |
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Collana |
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Wiley Series in Probability and Statistics., Texts, References, and Pocketbooks Section |
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Disciplina |
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Soggetti |
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Linear models (Statistics) |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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CONTENTS; PREFACE; 1 INTRODUCTION; 1.1 MODELS; a. Linear models (LM) and linear mixed models (LMM); b. Generalized models (GLMs and GLMMs); 1.2 FACTORS, LEVELS, CELLS, EFFECTS AND DATA; 1.3 FIXED EFFECTS MODELS; a. Example 1: Placebo and a drug; b. Example 2: Comprehension of humor; c. Example 3: Four dose levels of a drug; 1.4 RANDOM EFFECTS MODELS; a. Example 4: Clinics; b. Notation; i. Properties of random effects in LMMs; ii. The notation of mathematical statistics; iii. Variance of y; iv. Variance and conditional expected values; c. Example 5: Ball bearings and calipers |
1.5 LINEAR MIXED MODELS (LMMs)a. Example 6: Medications and clinics; b. Example 7: Drying methods and fabrics; c. Example 8: Potomac River Fever; d. Regression models; e. Longitudinal data; f. Model equations; 1.6 FIXED OR RANDOM?; a. Example 9: Clinic effects; b. Making a decision; 1.7 INFERENCE; a. Estimation; i. Maximum likelihood (ML); ii. Restricted maximum likelihood (REML); iii. Solutions |
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and estimators; iv. Bayes theorem; v. Quasi-likelihood estimation; vi. Generalized estimating equations; b. Testing; i. Likelihood ratio test (LRT); ii. Wald's procedure; c. Prediction |
1.8 COMPUTER SOFTWARE1.9 EXERCISES; 2 ONE-WAY CLASSIFICATIONS; 2.1 NORMALITY AND FIXED EFFECTS; a. Model; b. Estimation by ML; c. Generalized likelihood ratio test; d. Confidence intervals; i. For means; ii. For differences in means; iii. For linear combinations; iv. For the variance; e. Hypothesis tests; 2.2 NORMALITY, RANDOM EFFECTS AND ML; a. Model; i. Covariances caused by random effects; ii. Likelihood; b. Balanced data; i. Likelihood; ii. ML equations and their solutions; iii. ML estimators; iv. Expected values and bias; v. Asymptotic sampling variances; vi. REML estimation |
c. Unbalanced datai. Likelihood; ii. ML equations and their solutions; iii. ML estimators; d. Bias; e. Sampling variances; 2.3 NORMALITY, RANDOM EFFECTS AND REML; a. Balanced data; i. Likelihood; ii. REML equations and their solutions; iii. REML estimators; iv. Comparison with ML; v. Bias; vi. Sampling variances; b. Unbalanced data; 2.4 MORE ON RANDOM EFFECTS AND NORMALITY; a. Tests and confidence intervals; i. For the overall mean, μ; ii. For σ[sup(2)]; iii. For σ[sup(2)][sub(a)]; b. Predicting random effects; i. A basic result; ii. In a 1-way classification |
2.5 BERNOULLI DATA: FIXED EFFECTSa. Model equation; b. Likelihood; c. ML equations and their solutions; d. Likelihood ratio test; e. The usual chi-square test; f. Large-sample tests and intervals; g. Exact tests and confidence intervals; h. Example: Snake strike data; 2.6 BERNOULLI DATA: RANDOM EFFECTS; a. Model equation; b. Beta-binomial model; i. Means, variances, and covariances; ii. Overdispersion; iii. Likelihood; iv. ML estimation; v. Large-sample variances; vi. Large-sample tests and intervals; vii. Prediction; c. Legit-normal model; i. Likelihood; ii. Calculation of the likelihood |
iii. Means, variances, and covariances |
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Sommario/riassunto |
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Wiley Series in Probability and StatisticsA modern perspective on mixed modelsThe availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data.As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses |
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