Advanced Regression Models with SAS and R

Description

Advanced Regression Models with SAS and R exposes the reader to the modern world of regression analysis. The material covered by this book consists of regression models that go beyond linear regression, including models for right-skewed, categorical and hierarchical observations. The book presents the theory as well as fully worked-out numerical examples with complete SAS and R codes for each regression. The emphasis is on model accuracy and the interpretation of results. For each regression, the fitted model is presented along with interpretation of estimated regression coefficients and prediction of response for given values of predictors. Features: Presents the theoretical framework for each regression. Discusses data that are categorical, count, proportions, right-skewed, longitudinal and hierarchical. Uses examples based on real-life consulting projects. Provides complete SAS and R codes for each example. Includes several exercises for every regression. Advanced Regression Models with SAS and R is designed as a text for an upper division undergraduate or a graduate course in regression analysis. Prior exposure to the two software packages is desired but not required. The Author: Olga Korosteleva is a Professor of Statistics at California State University, Long Beach. She teaches a large variety of statistical courses to undergraduate and master’s students. She has published three statistical textbooks. For a number of years, she has held the position of faculty director of the statistical consulting group. Her research interests lie mostly in applications of statistical methodology through collaboration with her clients in health sciences, nursing, kinesiology, and other fields. Cover Half Title Title Copyright Contents Preface Chapter 1 Introduction: General and Generalized Linear Regression Models 1.1 Definition of General Linear Regression Model 1.2 Definition of Generalized Linear Regression Model 1.3 Parameter Estimation and Significance Test for Coefficients 1.4 Fitted Model 1.5 Interpretation of Estimated Regression Coefficients 1.6 Model Goodness-of-Fit Check 1.7 Predicted Response 1.8 SAS Implementation 1.9 R Implementation 1.10 Example Exercises Chapter 2 Regression Models for Response with Right-skewed Distribution 2.1 Box-Cox Power Transformation 2.1.1 Model Definition 2.1.2 Fitted Model 2.1.3 Interpretation of Estimated Regression Coefficients 2.1.4 Predicted Response 2.1.5 SAS Implementation 2.1.6 R Implementation 2.1.7 Example 2.2 Gamma Regression Model 2.2.1 Model Definition 2.2.2 Fitted Model 2.2.3 Interpretation of Estimated Regression Coefficients 2.2.4 Predicted Response 2.2.5 SAS Implementation 2.2.6 R Implementation 2.2.7 Example Exercises Chapter 3 Regression Models for Binary Response 3.1 Binary Logistic Regression Model 3.1.1 Model Definition 3.1.2 Fitted Model 3.1.3 Interpretation of Estimated Regression Coefficients 3.1.4 Predicted Probability 3.1.5 SAS Implementation 3.1.6 R Implementation 3.1.7 Example 3.2 Probit Model 3.2.1 Model Definition 3.2.2 Fitted Model 3.2.3 Interpretation of Estimated Regression Coefficients 3.2.4 Predicted Probability 3.2.5 SAS Implementation 3.2.6 R Implementation 3.2.7 Example 3.3 Complementary Log-Log Model 3.3.1 Model Definition 3.3.2 Fitted Model 3.3.3 Interpretation of Estimated Regression Coefficients 3.3.4 Predicted Probability 3.3.5 SAS Implementation 3.3.6 R Implementation 3.3.7 Example Exercises Chapter 4 Regression Models for Categorical Response 4.1 Cumulative Logit Model 4.1.1 Model Definition 4.1.2 Fitted Model 4.1.3 Interpretation of Estimated Regression Coefficients 4.1.4 Predicted Probabilities 4.1.5 SAS Implementation 4.1.6 R Implementation 4.1.7 Example 4.2 Cumulative Probit Model 4.2.1 Model Definition 4.2.2 Fitted Model 4.2.3 Interpretation of Estimated Regression Coefficients 4.2.4 Predicted Probabilities 4.2.5 SAS Implementation 4.2.6 R Implementation 4.2.7 Example 4.3 Cumulative Complementary Log-Log Model 4.3.1 Model Definition 4.3.2 Fitted Model 4.3.3 Interpretation of Estimated Regression Coefficients 4.3.4 Predicted Probabilities 4.3.5 SAS Implementation 4.3.6 R Implementation 4.3.7 Example 4.4 Generalized Logit Model for Nominal Response 4.4.1 Model Definition 4.4.2 Fitted Model 4.4.3 Interpretation of Estimated Regression Coefficients 4.4.4 Predicted Probabilities 4.4.5 SAS Implementation 4.4.6 R Implementation 4.4.7 Example Exercises Chapter 5 Regression Models for Count Response 5.1 Poisson Regression Model 5.1.1 Model Definition 5.1.2 Fitted Model 5.1.3 Interpretation of Estimated Regression Coefficients 5.1.4 Predicted Response 5.1.5 SAS Implementation 5.1.6 R Implementation 5.1.7 Example 5.2 Zero-truncated Poisson Regression Model 5.2.1 Model Definition 5.2.2 Fitted Model 5.2.3 Interpretation of Estimated Regression Coefficients 5.2.4 Predicted Response 5.2.5 SAS Implementation 5.2.6 R Implementation 5.2.7 Example 5.3 Zero-inflated Poisson Regression Model 5.3.1 Model Definition 5.3.2 Fitted Model 5.3.3 Interpretation of Estimated Regression Coefficients 5.3.4 Predicted Response 5.3.5 SAS Implementation 5.3.6 R Implementation 5.3.7 Example 5.4 Hurdle Poisson Regression Model 5.4.1 Model Definition 5.4.2 Fitted Model 5.4.3 Interpretation of Estimated Regression Coefficients 5.4.4 Predicted Response 5.4.5 SAS Implementation 5.4.6 R Implementation 5.4.7 Example Exercises Chapter 6 Regression Models for Overdispersed Count Response 6.1 Negative Binomial Regression Model 6.1.1 Model Definition 6.1.2 Fitted Model 6.1.3 Interpretation of Estimated Regression Coefficients 6.1.4 Predicted Response 6.1.5 SAS Implementation 6.1.6 R Implementation 6.1.7 Example 6.2 Zero-truncated Negative Binomial Regression Model 6.2.1 Model Definition 6.2.2 Fitted Model 6.2.3 Interpretation of Estimated Regression Coefficients 6.2.4 Predicted Response 6.2.5 SAS Implementation 6.2.6 R Implementation 6.2.7 Example 6.3 Zero-inflated Negative Binomial Regression Model 6.3.1 Model Definition 6.3.2 Fitted Model 6.3.3 Interpretation of Estimated Regression Coefficients 6.3.4 Predicted Response 6.3.5 SAS Implementation 6.3.6 R Implementation 6.3.7 Example 6.4 Hurdle Negative Binomial Regression Model 6.4.1 Model Definition 6.4.2 Fitted Model 6.4.3 Interpretation of Estimated Regression Coefficients 6.4.4 Predicted Response 6.4.5 SAS Implementation 6.4.6 R Implementation 6.4.7 Example Exercises Chapter 7 Regression Models for Proportion Response 7.1 Beta Regression Model 7.1.1 Model Definition 7.1.2 Fitted Model 7.1.3 Interpretation of Estimated Regression Coefficients 7.1.4 Predicted Response 7.1.5 SAS Implementation 7.1.6 R Implementation 7.1.7 Example 7.2 Zero-inflated Beta Regression Model 7.2.1 Model Definition 7.2.2 Fitted Model 7.2.3 Interpretation of Estimated Regression Coefficients 7.2.4 Predicted Response 7.2.5 SAS Implementation 7.2.6 R Implementation 7.2.7 Example 7.3 One-inflated Beta Regression Model 7.3.1 Model Definition 7.3.2 Fitted Model 7.3.3 Interpretation of Estimated Regression Coefficients 7.3.4 Predicted Response 7.3.5 SAS Implementation 7.3.6 R Implementation 7.3.7 Example 7.4 Zero-one-inflated Beta Regression Model 7.4.1 Model Definition 7.4.2 Fitted Model 7.4.3 Interpretation of Estimated Regression Coefficients 7.4.4 Predicted Response 7.4.5 SAS Implementation 7.4.6 R Implementation 7.4.7 Example Exercises Chapter 8 General Linear Regression Models for Repeated Measures Data 8.1 Random Slope and Intercept Model 8.1.1 Model Definition 8.1.2 Fitted Model 8.1.3 Interpretation of Estimated Regression Coefficients 8.1.4 Model Goodness-of-Fit Check 8.1.5 Predicted Response 8.1.6 SAS Implementation 8.1.7 R Implementation 8.1.8 Example 8.2 Random Slope and Intercept Model with Covariance Structure for Error 8.2.1 Model Definition 8.2.2 Fitted Model, Interpretation of Estimated Regression Coefficients, and Predicted Response 8.2.3 Model Goodness-of-fit Check 8.2.4 SAS Implementation 8.2.5 R Implementation 8.2.6 Example 8.3 Generalized Estimating Equations Model 8.3.1 Model Definition 8.3.2 Fitted Model, Interpretation of Estimated Regression Coefficients, and Predicted Response 8.3.3 Model Goodness-of-Fit Check 8.3.4 SAS Implementation 8.3.5 R Implementation 8.3.6 Example Exercises Chapter 9 Generalized Linear Regression Models for Repeated Measures Data 9.1 Generalized Random Slope and Intercept Model 9.1.1 Model Definition 9.1.2 Fitted Model, Interpretation of Estimated Regression Coefficients, Model Goodness-of-Fit Check, and Predicted Response 9.1.3 SAS Implementation 9.1.4 R Implementation 9.1.5 Example 9.2 Generalized Estimating Equations Model 9.2.1 Model Definition 9.2.2 SAS Implementation 9.2.3 R Implementation 9.2.4 Example Exercises Chapter 10 Hierarchical Regression Model 10.1 Hierarchical Regression Model for Normal Response 10.1.1 Model Definition 10.1.2 Fitted Model, Interpretation of Estimated Regression Coefficients, Model Goodness-of-Fit Check, Predicted Response 10.1.3 SAS Implementation 10.1.4 R Implementation 10.1.5 Example 10.2 Hierarchical Regression Model for Non-normal Response 10.2.1 Model Definition 10.2.2 Fitted Model 10.2.3 Interpretation of Estimated Regression Coefficients 10.2.4 Model Goodness-of-Fit Check 10.2.5 Predicted Response 10.2.6 SAS Implementation 10.2.7 R Implementation 10.2.8 Example Exercises Recommended Books List of Notation Subject Index