Beyond Multiple Linear Regression-Applied Generalized Linear Models and Multilevel Models in R

Description

Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner. The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling. A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR) Table of Contents Review of Multiple Linear Regression Learning Objectives Introduction to Beyond Multiple Linear Regression Assumptions for Linear Least Squares Regression (LLSR) Cases that do not violate assumptions for inference in LLSR Cases where assumptions for inference in LLSR are violated Review of Multiple Linear Regression Case Study: Kentucky Derby Initial Exploratory Analyses Data Organization Univariate Summaries Bivariate Summaries Multiple linear regression modeling Simple linear regression with a continuous predictor Linear regression with a binary predictor Multiple linear regression with two predictors Inference in multiple linear regression: normal theory Inference in multiple linear regression: bootstrapping Multiple linear regression with an interaction term Building a multiple linear regression model Preview of remaining chapters Soccer Elephant Mating Parenting and Gang Activity Crime Exercises Conceptual Exercises Guided Exercises Open-ended Exercises Beyond Least Squares: Using Likelihoods to Fit and Compare Models Learning Objectives Case Study: Does sex run in families? Research Questions Model: Sex Unconditional Model (Equal probabilities, Independence) Model: Sex Unconditional Model (Any Probability, Independence) What is a likelihood? Finding MLEs Summary Is a likelihood a probability function? (Optional) Model: Sex Conditional Model (Sex Bias) Model Specification Application to Hypothetical Data Case Study: Analysis of the NLSY data Model Building Plan Family Composition of Boys and Girls, NLSY: Exploratory Data Analysis Likelihood for the Sex Unconditional Model: the NLSY data Likelihood for the Sex Conditional Model Comparing the Sex Unconditional to the Sex Conditional Model Model: Stopping Rule Model (Waiting for a boy) Non-nested Models Summary of Model Building Likelihood-based Methods Likelihoods and this Course Exercises Conceptual Exercises Guided Exercises Open-ended Exercise Distribution Theory Learning Objectives Introduction Discrete Random Variables Binary Random Variable Binomial Random Variable Geometric Random Variable Negative Binomial Random Variable Hypergeometric Random Variable Poisson Random Variable Continuous Random Variables Exponential Random Variable Gamma Random Variable Normal (Gaussian) Random Variable Beta Random Variable Distributions used in Testing □□ Distribution Student’s □□・Distribution □□ ・Distribution Additional Resources Exercises Conceptual Exercises Guided Exercises Poisson Regression Learning Objectives Introduction to Poisson Regression Poisson Regression Assumptions A Graphical Look at Poisson Regression Case Studies Overview Case Study: Household Size in the Philippines Data Organization Exploratory Data Analyses Estimation and Inference Using Deviances to Compare Models Using Likelihoods to fit Poisson Regression Models (Optional) Second Order Model Adding a covariate Residuals for Poisson Models (Optional) Goodness-of-fit Linear Least Squares Regression vs Poisson Regression Case Study: Campus Crime Data Organization Exploratory Data Analysis Accounting for Enrollment Modeling Assumptions Initial Models Tukey’s Honestly Significant Differences Overdispersion Dispersion parameter adjustment No dispersion vs overdispersion Negative binomial modeling Case Study: Weekend drinking Research Question Data Organization Exploratory Data Analysis Modeling Fitting a ZIP Model Comparing ZIP to ordinary Poisson with the Vuong Test (Optional) Residual Plot Limitations Exercises Conceptual Exercises Guided Exercises Open-ended Exercises Generalized Linear Models (GLMs): A Unifying Theory Learning Objectives One parameter exponential families One Parameter Exponential Family: Possion One parameter exponential family: Normal Generalized Linear Modeling Exercises Logistic Regression Learning Objectives Introduction to Logistic Regression Logistic Regression Assumptions A Graphical Look at Logistic Regression Case Studies Overview Case Study: Soccer Goalkeepers Modeling Odds Logistic Regression Models for Binomial Responses Theoretical rationale for logistic regression models (Optional) Case Study: Reconstructing Alabama Data Organization Exploratory Analyses Initial Models Tests for significance of model coefficients Confidence intervals for model coefficients Testing for goodness of fit Residuals for Binomial Regression Overdispersion Summary Linear Least Squares Regression vs Binomial Logistic Regression Case Study: Trying to Lose Weight Data Organization Exploratory Data Analysis Initial Models Drop-in-deviance Tests Model Discussion and Summary Exercises Conceptual Exercises Guided Exercises Open-ended Exercises Correlated Data Learning Objectives Introduction Recognizing correlation Case Study: Dams and pups Sources of Variability Scenario: No covariates Scenario: Dose effect Case Study: Tree Growth Format of the data set Sources of variability Analysis preview: accounting for correlation within transect Summary Exercises Conceptual Exercises Guided Exercises Note on Correlated Binary Outcomes Introduction to Multilevel Models Learning Objectives Case Study: Music Performance Anxiety Initial Exploratory Analyses Data Organization Exploratory Analyses: Univariate Summaries Exploratory Analyses: Bivariate Summaries Two level modeling: preliminary considerations Ignoring the two level structure (not recommended) A two-stage modeling approach (better but imperfect) Two level modeling: a unified approach Our framework Random vs fixed effects Distribution of errors: the multivariate normal distribution Technical issues when estimating and testing parameters (Optional) An initial model with parameter interpretations Building a multilevel model Model building strategy An initial model: unconditional means or random intercepts Binary covariates at Level One and Level Two Random slopes and intercepts model Pseudo □□ values Adding a covariate at Level Two Additional covariates: model comparison and interpretability Interpretation of parameter estimates Model comparisons Center covariates A potential final model for music performance anxiety Modeling the multilevel structure: is it really necessary? Notes on Using R (Optional) Exercises Conceptual Exercises Guided Exercise Open-ended Exercises Two Level Longitudinal Data Learning objectives Case study: Charter schools Initial Exploratory Analyses Data organization Missing data Exploratory analyses for general multilevel models Exploratory analyses for longitudinal data Preliminary two-stage modeling Linear trends within schools Effects of level two covariates on linear time trends Error structure within schools Initial models Unconditional means model Unconditional growth model Modeling other trends over time Building to a final model Uncontrolled effects of school type Add percent free and reduced lunch as a covariate A potential final model with three Level Two covariates Parametric bootstrap testing Covariance structure among observations Standard covariance structure Alternative covariance structures Covariance structure in non-longitudinal multilevel models Final thoughts regarding covariance structures Details of covariance structures (Optional) Notes on Using R (Optional) Exercises Conceptual Exercises Guided Exercise Open-ended Exercises Multilevel Data With More Than Two Levels Learning Objectives Case Studies: Seed Germination Initial Exploratory Analyses Data Organization Exploratory Analyses Initial models: unconditional means and unconditional growth Encountering boundary constraints Parametric bootstrap testing Exploding variance components Building to a final model Covariance structure (Optional) Details of covariance structures Notes on Using R (Optional) Exercises Conceptual Exercises Guided Exercises Open-ended Exercises Multilevel Generalized Linear Models Learning Objectives Case Study: College Basketball Referees Initial Exploratory Analyses Data organization Exploratory analyses Two level Modeling with a Generalized Response A GLM approach (correlation not accounted for) A two-stage modeling approach (provides the basic idea for multilevel modeling) A unified multilevel approach (the framework we’ll use) Crossed Random Effects Model Comparisons Using the Parametric Bootstrap A Potential Final Model for Examining Referee Bias Estimated Random Effects Notes on Using R (Optional) Exercises Conceptual Exercises Open-ended Exercises