Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Second Edition(Chapman & Hall/CRC Texts in Statistical Science)

Analysis of Variance, Design, and Regression: Linear Modeling for Unbalanced Data, Second Edition presents linear structures for modeling data with an emphasis on how to incorporate specific ideas (hypotheses) about the structure of the data into a linear model for the data. The book carefully analyzes small data sets by using tools that are easily scaled to big data. The tools also apply to small relevant data sets that are extracted from big data. New to the Second Edition Reorganized to focus on unbalanced data Reworked balanced analyses using methods for unbalanced data Introductions to nonparametric and lasso regression Introductions to general additive and generalized additive models Examination of homologous factors Unbalanced split plot analyses Extensions to generalized linear models R, Minitab®, and SAS code on the author’s website The text can be used in a variety of courses, including a yearlong graduate course on regression and ANOVA or a data analysis course for upper-division statistics students and graduate students from other fields. It places a strong emphasis on interpreting the range of computer output encountered when dealing with unbalanced data.

Table of Contents:
Introduction Probability Random variables and expectations Continuous distributions The binomial distribution The multinomial distribution One Sample Example and introduction Parametric inference about μ Prediction intervals Model testing Checking normality Transformations Inference about σ2 General Statistical Inference Model-based testing Inference on single parameters: assumptions Parametric tests Confidence intervals P values Validity of tests and confidence intervals Theory of prediction intervals Sample size determination and power The shape of things to come Two Samples Two correlated samples: Paired comparisons Two independent samples with equal variances Two independent samples with unequal variances Testing equality of the variances Contingency Tables One binomial sample Two independent binomial samples One multinomial sample Two independent multinomial samples Several independent multinomial samples Lancaster–Irwin partitioning Simple Linear Regression An example The simple linear regression model The analysis of variance table Model-based inference Parametric inferential procedures An alternative model Correlation Two-sample problems A multiple regression Estimation formulae for simple linear regression Model Checking Recognizing randomness: Simulated data with zero correlation Checking assumptions: Residual analysis Transformations Lack of Fit and Nonparametric Regression Polynomial regression Polynomial regression and leverages Other basis functions Partitioning methods Splines Fisher’s lack-of-fit test Multiple Regression: Introduction Example of inferential procedures Regression surfaces and prediction Comparing regression models Sequential fitting Reduced models and prediction Partial correlation coefficients and added variable plots Collinearity More on model testing Additive effects and interaction Generalized additive models Final comment Diagnostics and Variable Selection Diagnostics Best subset model selection Stepwise model selection Model selection and case deletion Lasso regression Multiple Regression: Matrix Formulation Random vectors Matrix formulation of regression models Least squares estimation of regression parameters Inferential procedures Residuals, standardized residuals, and leverage Principal components regression One-Way ANOVA Example Theory Regression analysis of ANOVA data Modeling contrasts Polynomial regression and one-way ANOVA Weighted least squares Multiple Comparison Methods "Fisher’s" least significant difference method Bonferroni adjustments Scheffé’s method Studentized range methods Summary of multiple comparison procedures Two-Way ANOVA Unbalanced two-way analysis of variance Modeling contrasts Regression modeling Homologous factors ACOVA and Interactions One covariate example Regression modeling ACOVA and two-way ANOVA Near replicate lack-of-fit tests Multifactor Structures Unbalanced three-factor analysis of variance Balanced three-factors Higher-order structures Basic Experimental Designs Experiments and causation Technical design considerations Completely randomized designs Randomized complete block designs Latin square designs Balanced incomplete block designs Youden squares Analysis of covariance in designed experiments Discussion of experimental design Factorial Treatments Factorial treatment structures Analysis Modeling factorials Interaction in a Latin square A balanced incomplete block design Extensions of Latin squares Dependent Data The analysis of split-plot designs A four-factor example Multivariate analysis of variance Random effects models Logistic Regression: Predicting Counts Models for binomial data Simple linear logistic regression Model testing Fitting logistic models Binary data Multiple logistic regression ANOVA type logit models Ordered categories Log-Linear Models: Describing Count Data Models for two-factor tables Models for three-factor tables Estimation and odds ratios Higher-dimensional tables Ordered categories Offsets Relation to logistic models Multinomial responses Logistic discrimination and allocation Exponential and Gamma Regression: Time-to-Event Data Exponential regression Gamma regression Nonlinear Regression Introduction and examples Estimation Statistical inference Linearizable models Appendix A: Matrices and Vectors Appendix B: Tables Exercises appear at the end of each chapter.