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Beyond Multiple Linear Regression: Applied Generalized Linear Models And Multilevel Models in R

Beyond Multiple Linear Regression: Applied Generalized Linear Models And Multilevel Models in R

Authors
Publisher Taylor & Francis Inc
Year 18/12/2020
Pages 418
Version hardback
Readership level College/higher education
ISBN 9781439885383
Categories Psychological methodology, Probability & statistics, Biology, life sciences
$136.00 (with VAT)
500.00 PLN / €111.50 / £95.79
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Book 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)

Beyond Multiple Linear Regression: Applied Generalized Linear Models And Multilevel Models in R

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

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