Showing papers on "Random effects model published in 1977"

An introduction to statistical methods and data analysis

Abstract: PART I: INTRODUCTION 1. WHAT IS STATISTICS? Introduction / Why Study Statistics? / Some Current Applications of Statistics / What Do Statisticians Do? / Quality and Process Improvement / A Note to the Student / Summary / Supplementary Exercises PART II: COLLECTING THE DATA 2. USING SURVEYS AND SCIENTIFIC STUDIES TO COLLECT DATA Introduction / Surveys / Scientific Studies / Observational Studies / Data Management: Preparing Data for Summarization and Analysis / Summary PART III: SUMMARIZING DATA 3. DATA DESCRIPTION Introduction / Describing Data on a Single Variable: Graphical Methods / Describing Data on a Single Variable: Measures of Central Tendency / Describing Data on a Single Variable: Measures of Variability / The Box Plot / Summarizing Data from More Than One Variable / Calculators, Computers, and Software Systems / Summary / Key Formulas / Supplementary Exercises PART IV: TOOLS AND CONCEPTS 4. PROBABILITY AND PROBABILITY DISTRIBUTIONS How Probability Can Be Used in Making Inferences / Finding the Probability of an Event / Basic Event Relations and Probability Laws / Conditional Probability and Independence / Bayes's Formula / Variables: Discrete and Continuous / Probability Distributions for Discrete Random Variables / A Useful Discrete Random Variable: The Binomial / Probability Distributions for Continuous Random Variables / A Useful Continuous Random Variable: The Normal Distribution / Random Sampling / Sampling Distributions / Normal Approximation to the Binomial / Summary / Key Formulas / Supplementary Exercises PART V: ANALYZING DATA: CENTRAL VALUES, VARIANCES, AND PROPORTIONS 5. INFERENCES ON A POPULATION CENTRAL VALUE Introduction and Case Study / Estimation of / Choosing the Sample Size for Estimating / A Statistical Test for / Choosing the Sample Size for Testing / The Level of Significance of a Statistical Test / Inferences about for Normal Population, s Unknown / Inferences about the Population Median / Summary / Key Formulas / Supplementary Exercises 6. COMPARING TWO POPULATION CENTRAL VALUES Introduction and Case Study / Inferences about 1 - 2: Independent Samples / A Nonparametric Alternative: The Wilcoxon Rank Sum Test / Inferences about 1 - 2: Paired Data / A Nonparametric Alternative: The Wilcoxon Signed-Rank Test / Choosing Sample Sizes for Inferences about 1 - 2 / Summary / Key Formulas / Supplementary Exercises 7. INFERENCES ABOUT POPULATION VARIANCES Introduction and Case Study / Estimation and Tests for a Population Variance / Estimation and Tests for Comparing Two Population Variances / Tests for Comparing k > 2 Population Variances / Summary / Key Formulas / Supplementary Exercises 8. INFERENCES ABOUT POPULATION CENTRAL VALUES Introduction and Case Study / A Statistical Test About More Than Two Population Variances / Checking on the Assumptions / Alternative When Assumptions are Violated: Transformations / A Nonparametric Alternative: The Kruskal-Wallis Test / Summary / Key Formulas / Supplementary Exercises 9. MULTIPLE COMPARISONS Introduction and Case Study / Planned Comparisons Among Treatments: Linear Contrasts / Which Error Rate Is Controlled / Multiple Comparisons with the Best Treatment / Comparison of Treatments to a Control / Pairwise Comparison on All Treatments / Summary / Key Formulas / Supplementary Exercises 10. CATEGORICAL DATA Introduction and Case Study / Inferences about a Population Proportion p / Comparing Two Population Proportions p1 - p2 / Probability Distributions for Discrete Random Variables / The Multinomial Experiment and Chi-Square Goodness-of-Fit Test / The Chi-Square Test of Homogeneity of Proportions / The Chi-Square Test of Independence of Two Nominal Level Variables / Fisher's Exact Test, a Permutation Test / Measures of Association / Combining Sets of Contingency Tables / Summary / Key Formulas / Supplementary Exercises PART VI: ANALYZING DATA: REGRESSION METHODS, MODEL BUILDING 11. SIMPLE LINEAR REGRESSION AND CORRELATION Linear Regression and the Method of Least Squares / Transformations to Linearize Data / Correlation / A Look Ahead: Multiple Regression / Summary of Key Formulas. Supplementary Exercises. 12. INFERENCES RELATED TO LINEAR REGRESSION AND CORRELATION Introduction and Case Study / Diagnostics for Detecting Violations of Model Conditions / Inferences about the Intercept and Slope of the Regression Line / Inferences about the Population Mean for a Specified Value of the Explanatory Variable / Predictions and Prediction Intervals / Examining Lack of Fit in the Model / The Inverse Regression Problem (Calibration): Predicting Values for x for a Specified Value of y / Summary / Key Formulas / Supplementary Exercises 13. MULTIPLE REGRESSION AND THE GENERAL LINEAR MODEL Introduction and Case Study / The General Linear Model / Least Squares Estimates of Parameters in the General Linear Model / Inferences about the Parameters in the General Linear Model / Inferences about the Population Mean and Predictions from the General Linear Model / Comparing the Slope of Several Regression Lines / Logistic Regression / Matrix Formulation of the General Linear Model / Summary / Key Formulas / Supplementary Exercises 14. BUILDING REGRESSION MODELS WITH DIAGNOSTICS Introduction and Case Study / Selecting the Variables (Step 1) / Model Formulation (Step 2) / Checking Model Conditions (Step 3) / Summary / Key Formulas / Supplementary Exercises PART VII: ANALYZING DATA: DESIGN OF EXPERIMENTS AND ANOVA 15. DESIGN CONCEPTS FOR EXPERIMENTS AND STUDIES Experiments, Treatments, Experimental Units, Blocking, Randomization, and Measurement Units / How Many Replications? / Studies for Comparing Means versus Studies for Comparing Variances / Summary / Key Formulas / Supplementary Exercises 16. ANALYSIS OF VARIANCE FOR STANDARD DESIGNS Introduction and Case Study / Completely Randomized Design with Single Factor / Randomized Block Design / Latin Square Design / Factorial Experiments in a Completely Randomized Design / The Estimation of Treatment Differences and Planned Comparisons in the Treatment Means / Checking Model Conditions / Alternative Analyses: Transformation and Friedman's Rank-Based Test / Summary / Key Formulas / Supplementary Exercises 17. ANALYSIS OF COVARIANCE Introduction and Case Study / A Completely Randomized Design with One Covariate / The Extrapolation Problem / Multiple Covariates and More Complicated Designs / Summary / Key Formulas / Supplementary Exercises 18. ANALYSIS OF VARIANCE FOR SOME UNBALANCED DESIGNS Introduction and Case Study / A Randomized Block Design with One or More Missing Observations / A Latin Square Design with Missing Data / Incomplete Block Designs / Summary / Key Formulas / Supplementary Exercises 19. ANALYSIS OF VARIANCE FOR SOME FIXED EFFECTS, RANDOM EFFECTS, AND MIXED EFFECTS MODELS Introduction and Case Study / A One-Factor Experiment with Random Treatment Effects / Extensions of Random-Effects Models / A Mixed Model: Experiments with Both Fixed and Random Treatment Effects / Models with Nested Factors / Rules for Obtaining Expected Mean Squares / Summary / Key Formulas / Supplementary Exercises 20. SPLIT-PLOT DESIGNS AND EXPERIMENTS WITH REPEATED MEASURES Introduction and Case Study / Split-Plot Designs / Single-Factor Experiments with Repeated Measures / Two-Factor Experiments with Repeated Measures on One of the Factors / Crossover Design / Summary / Key Formulas / Supplementary Exercises PART VIII: COMMUNICATING AND DOCUMENTING THE RESULTS OF A STUDY OR EXPERIMENT 21. COMMUNICATING AND DOCUMENTING THE RESULTS OF A STUDY OR EXPERIMENT Introduction / The Difficulty of Good Communication / Communication Hurdles: Graphical Distortions / Communication Hurdles: Biased Samples / Communication Hurdles: Sample Size / The Statistical Report / Documentation and Storage of Results / Summary / Supplementary Exercises

Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems

Abstract: Recent developments promise to increase greatly the popularity of maximum likelihood (ml) as a technique for estimating variance components. Patterson and Thompson (1971) proposed a restricted maximum likelihood (reml) approach which takes into account the loss in degrees of freedom resulting from estimating fixed effects. Miller (1973) developed a satisfactory asymptotic theory for ml estimators of variance components. There are many iterative algorithms that can be considered for computing the ml or reml estimates. The computations on each iteration of these algorithms are those associated with computing estimates of fixed and random effects for given values of the variance components.

A one-way components of variance model for categorical data

Abstract: A components of variance model for categorical data from unbalanced designs which is directly analogous to a one-way random effects ANO VA modelfor quantitative data is proposed. The variance components provide separate reliability measures for each of the response categories and disagreement measures between pairs of response categories in terms of (within subject) intraclass and interclass correlation coefficients. The estimation procedures involve usual MA NOVA calculations which can be expressed as compounded functions of the multinomial observations. Thus, the variances of these estimates can be obtainedfrom linearized Taylor series results. These procedures are illustrated with data from a psychiatric diagnosis study.

A Reformulation of Linear Models

Abstract: SUMMARY Dissatisfaction is expressed with aspects of the current exposition of linear models, including the neglect of marginality, unnecessary differences between models for finite and infinite populations, failure to distinguish different kinds of random terms, impositon of unnecessary and inconsistent constraints on parameters, and lack of an adequate notation for negative components of variance. The reformulation, exemplified for crossed and nested classifications of balanced data, and for simple orthogonal designed experiments, is designed to integrate finite and infinite populations, random and fixed effects, excess and deficit of variance, to avoid unnecessary constraints on parameters, and to lead naturally to interesting hypotheses about the model terms.

Factors for One-Sided Tolerance Limits for Balanced One-Way-ANOVA Random-Effects Model

Abstract: A technique based on the noncentral t distribution for obtaining one-sided tolerance limits for a balanced one-way-anova random-effects model is developed. These limits are such that the probability is γ that at least a proportion p of the population consisting of very many specimens from very many batches exceeds the calculated lower limit. A few selected tables are given, and an example illustrates the use of the derived tolerance factors.

A two-stage model for growth curves which leads to Rao's covariance adjusted estimators

Abstract: SUMMARY It is well known that the unweighted estimator for growth curve parameters may be justified by a random effects model. We show that the more complicated adjusted estimators suggested by Rao may also be justified in terms of a two-stage model whose interprQtation is simple. In studying growth it is common to make several observations over a period of time on each of the individuals in the study. If an average growth curve is then fitted to such data it is necessary to allow for the dependence between observations on the same individual. In the simplest cases this leads to a regression model with covariance: with the usual notation we have, independently,

An Investigation into Interviewer Effects in Market Research

Abstract: Results of a survey of attitudes toward a range of potential new products are analyzed to detect interviewer effects by means of a nested random effects analysis of variance model. The relationship...

Power aspects of analysis of variance in random effects models A simulation study

Abstract: The effect of non‐normality on the power in analysis of variance for a random effect model is discussed by a simulation method. One and two‐way classifications are considered for this model and the erlangian and contaminated normal distributions are taken as examples of non‐normality. The results obtained by these methods are given in tables 1 and 2 which indicate that non‐normality has little effect on the power of the test.

Estimators for "the fraction of variance explained" in the one-way classification

Abstract: This paper deals with the estimation of "the fraction of variance expiained" in one-way classification. A comparative study of two estimators for model II (random effects) is made by computing approximately their biases and mean-square errors in the balanced case. A similar study is made for model I (fixed effects) where we study one estimator and give asymptotic formulae for its bias and mean-square error.

Random Effects in Biomedical Flow Systems

Abstract: The random effects in tracer kinetics and cell cycle kinetics are usually described by the particle residence time. An analytical framework is developed, and the importance of the statistical independence of the residence times is emphasized.

Bayesian estimation of means in a three component hierarchical design with random effect model

Abstract: The problem of estimating the means in a three component hierarchical random effect model yijk = μ + αi + βij + eijk is considered from a Bayesian view point. Posterior distributions of αi and βij are obtained under the assumptions that the αi are independently drawn from N(O,σ32), the βij are independently drawn from N(O,σ22) and the eijk are independent random errors from N(O,σ12) and adopting a non-informative reference prior distribution for μ, σ12, σ22, σ32. Various features of these posterior distributions are compared with the posterior distributions for a fixed effect model.