Advanced Regression Models with SAS and R

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.

1 Introduction: General and Generalized Linear Regression Models Definition of General Linear Regression Model Definition of Generalized Linear Regression Model Parameter Estimation and Significance Test for Coefficients Fitted Model Interpretation of Estimated Regression Coefficients Model Goodness-of-Fit Check Predicted Response SAS Implementation R Implementation Example Exercises 2 Regression Models for Response with Right-skewed Distribution Box-Cox Power Transformation Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Gamma Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Exercises 3 Regression Models for Binary Response Binary Logistic Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Probability SAS Implementation R Implementation Example Prohibit Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Probability SAS Implementation R Implementation Example Complementary Log-Log Model Model Definition and Development Fitted Model Interpretation of Estimated Regression Coefficients Predicted Probability SAS Implementation R Implementation Example Exercises 4 Regression Models for Categorical Response Cumulative Logit Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Probabilities SAS Implementation R Implementation Example Cumulative Prohibit Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients 2 Predicted Probabilities SAS Implementation R Implementation Example Cumulative Complementary Log-Log Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Probabilities SAS Implementation R Implementation Example Generalized Logit Model for Nominal Response Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Probabilities SAS Implementation R Implementation Example Exercises 5 Regression Models for Count Response Poisson Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Zero-truncated Poisson Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response Implementation R Implementation Example Zero-inflated Poisson Regression Model Model Definition Fitted Model 3 Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Hurdle Poisson Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Exercises 6 Regression Models for Over-Dispersed Count Response Negative Binomial Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Zero-truncated Negative Binomial Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Zero-inflated Negative Binomial Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Hurdle Negative Binomial Regression Model Model Definition 4 Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Exercises 7 Regression Models for Proportion Response Beta Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Zero-inflated Beta Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example One-inflated Beta Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Zero-one-inflated Beta Regression Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Predicted Response SAS Implementation R Implementation Example Exercises 8 General Linear Regression Models for Repeated Measures Data Random Slope and Intercept Model Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Model Goodness-of-Fit Check Predicted Response SAS Implementation R Implementation Example Mixed Model with Covariance Structure for Error Model Definition Coefficients, and Predicted Response Model Goodness-of-_t Check SAS Implementation R Implementation Example Generalized Estimating Equations Model Model Definition Fitted Model Model Goodness-of-Fit Check SAS Implementation R Implementation Example Exercises 9 Generalized Linear Regression Model for Repeated Measures Data Generalized Linear Mixed Model Models Definition Fitted Model, Interpretation, Prediction Model Goodness-of-Fit Check SAS Implementation R Implementation Example Generalized Estimating Equations Model Model Definition SAS Implementation R Implementation Example Exercises 10 Hierarchical Regression Model Hierarchical Regression Model for Normal Response Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Model Goodness-of-Fit Check Predicted Response SAS Implementation R Implementation Example Hierarchical Regression Model for Other Distributions Model Definition Fitted Model Interpretation of Estimated Regression Coefficients Model Goodness-of-Fit Check Predicted Response SAS Implementation R Implementation Examples Exercises

Olga Korosteleva is an associate professor of statistics in the Department of Mathematics and Statistics at California State University, Long Beach (CSULB). She received a Ph.D. in statistics from Purdue University.