Data Analysis Using Regression and Multilevel/Hierarchical Models

ISBN-10: 052168689X
ISBN-13: 9780521686891
Edition: 2006
List price: $69.99 Buy it from $43.71
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Description: Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety  More...

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Book details

List price: $69.99
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 12/18/2006
Binding: Paperback
Pages: 648
Size: 7.25" wide x 10.00" long x 1.75" tall
Weight: 2.706
Language: English

Data Analysis Using Regression and Multilevel/Hierarchical Models is a comprehensive manual for the applied researcher who wants to perform data analysis using linear and nonlinear regression and multilevel models. The book introduces a wide variety of models, whilst at the same time instructing the reader in how to fit these models using available software packages. The book illustrates the concepts by working through scores of real data examples that have arisen from the authors' own applied research, with programming codes provided for each one. Topics covered include causal inference, including regression, poststratification, matching, regression discontinuity, and instrumental variables, as well as multilevel logistic regression and missing-data imputation. Practical tips regarding building, fitting, and understanding are provided throughout.

List of examples
Preface
Why?
What is multilevel regression modeling?
Some examples from our own research
Motivations for multilevel modeling
Distinctive features of this book
Computing
Concepts and methods from basic probability and statistics
Probability distributions
Statistical inference
Classical confidence intervals
Classical hypothesis testing
Problems with statistical significance
55,000 residents desperately need your help!
Bibliographic note
Exercises
Single-level regression
Linear regression: the basics
One predictor
Multiple predictors
Interactions
Statistical inference
Graphical displays of data and fitted model
Assumptions and diagnostics
Prediction and validation
Bibliographic note
Exercises
Linear regression: before and after fitting the model
Linear transformations
Centering and standardizing, especially for models with interactions
Correlation and "regression to the mean"
Logarithmic transformations
Other transformations
Building regression models for prediction
Fitting a series of regressions
Bibliographic note
Exercises
Logistic regression
Logistic regression with a single predictor
Interpreting the logistic regression coefficients
Latent-data formulation
Building a logistic regression model: wells in Bangladesh
Logistic regression with interactions
Evaluating, checking, and comparing fitted logistic regressions
Average predictive comparisons on the probability scale
Identifiability and separation
Bibliographic note
Exercises
Generalized linear models
Introduction
Poisson regression, exposure, and overdispersion
Logistic-binomial model
Probit regression: normally distributed latent data
Ordered and unordered categorical regression
Robust regression using the t model
Building more complex generalized linear models
Constructive choice models
Bibliographic note
Exercises
Working with regression inferences
Simulation of probability models and statistical inferences
Simulation of probability models
Summarizing linear regressions using simulation: an informal Bayesian approach
Simulation for nonlinear predictions: congressional elections
Predictive simulation for generalized linear models
Bibliographic note
Exercises
Simulation for checking statistical procedures and model fits
Fake-data simulation
Example: using fake-data simulation to understand residual plots
Simulating from the fitted model and comparing to actual data
Using predictive simulation to check the fit of a time-series model
Bibliographic note
Exercises
Causal inference using regression on the treatment variable
Causal inference and predictive comparisons
The fundamental problem of causal inference
Randomized experiments
Treatment interactions and poststratification
Observational studies
Understanding causal inference in observational studies
Do not control for post-treatment variables
Intermediate outcomes and causal paths
Bibliographic note
Exercises
Causal inference using more advanced models
Imbalance and lack of complete overlap
Subclassification: effects and estimates for different subpopulations
Matching: subsetting the data to get overlapping and balanced treatment and control groups
Lack of overlap when the assignment mechanism is known: regression discontinuity
Estimating causal effects indirectly using instrumental variables
Instrumental variables in a regression framework
Identification strategies that make use of variation within or between groups
Bibliographic note
Exercises
Multilevel regression
Multilevel structures
Varying-intercept and varying-slope models
Clustered data: child support enforcement in cities
Repeated measurements, time-series cross sections, and other non-nested structures
Indicator variables and fixed or random effects
Costs and benefits of multilevel modeling
Bibliographic note
Exercises
Multilevel linear models: the basics
Notation
Partial pooling with no predictors
Partial pooling with predictors
Quickly fitting multilevel models in R
Five ways to write the same model
Group-level predictors
Model building and statistical significance
Predictions for new observations and new groups
How many groups and how many observations per group are needed to fit a multilevel model?
Bibliographic note
Exercises
Multilevel linear models: varying slopes, non-nested models, and other complexities
Varying intercepts and slopes
Varying slopes without varying intercepts
Modeling multiple varying coefficients using the scaled inverse-Wishart distribution
Understanding correlations between group-level intercepts and slopes
Non-nested models
Selecting, transforming, and combining regression inputs
More complex multilevel models
Bibliographic note
Exercises
Multilevel logistic regression
State-level opinions from national polls
Red states and blue states: what's the matter with Connecticut?
Item-response and ideal-point models
Non-nested overdispersed model for death sentence reversals
Bibliographic note
Exercises
Multilevel generalized linear models
Overdispersed Poisson regression: police stops and ethnicity
Ordered categorical regression: storable votes
Non-nested negative-binomial model of structure in social networks
Bibliographic note
Exercises
Fitting multilevel models
Multilevel modeling in Bugs and R: the basics
Why you should learn Bugs
Bayesian inference and prior distributions
Fitting and understanding a varying-intercept multilevel model using R and Bugs
Step by step through a Bugs model, as called from R
Adding individual- and group-level predictors
Predictions for new observations and new groups
Fake-data simulation
The principles of modeling in Bugs
Practical issues of implementation
Open-ended modeling in Bugs
Bibliographic note
Exercises
Fitting multilevel linear and generalized linear models in Bugs and R
Varying-intercept, varying-slope models
Varying intercepts and slopes with group-level predictors
Non-nested models
Multilevel logistic regression
Multilevel Poisson regression
Multilevel ordered categorical regression
Latent-data parameterizations of generalized linear models
Bibliographic note
Exercises
Likelihood and Bayesian inference and computation
Least squares and maximum likelihood estimation
Uncertainty estimates using the likelihood surface
Bayesian inference for classical and multilevel regression
Gibbs sampler for multilevel linear models
Likelihood inference, Bayesian inference, and the Gibbs sampler: the case of censored data
Metropolis algorithm for more general Bayesian computation
Specifying a log posterior density, Gibbs sampler, and Metropolis algorithm in R
Bibliographic note
Exercises
Debugging and speeding convergence
Debugging and confidence building
General methods for reducing computational requirements
Simple linear transformations
Redundant parameters and intentionally nonidentifiable models
Parameter expansion: multiplicative redundant parameters
Using redundant parameters to create an informative prior distribution for multilevel variance parameters
Bibliographic note
Exercises
Prom data collection to model understanding to model checking
Sample size and power calculations
Choices in the design of data collection
Classical power calculations: general principles, as illustrated by estimates of proportions
Classical power calculations for continuous outcomes
Multilevel power calculation for cluster sampling
Multilevel power calculation using fake-data simulation
Bibliographic note
Exercises
Understanding and summarizing the fitted models
Uncertainty and variability
Superpopulation and finite-population variances
Contrasts and comparisons of multilevel coefficients
Average predictive comparisons
R[superscript 2] and explained variance
Summarizing the amount of partial pooling
Adding a predictor can increase the residual variance!
Multiple comparisons and statistical significance
Bibliographic note
Exercises
Analysis of variance
Classical analysis of variance
ANOVA and multilevel linear and generalized linear models
Summarizing multilevel models using ANOVA
Doing ANOVA using multilevel models
Adding predictors: analysis of covariance and contrast analysis
Modeling the variance parameters: a split-plot latin square
Bibliographic note
Exercises
Causal inference using multilevel models
Multilevel aspects of data collection
Estimating treatment effects in a multilevel observational study
Treatments applied at different levels
Instrumental variables and multilevel modeling
Bibliographic note
Exercises
Model checking and comparison
Principles of predictive checking
Example: a behavioral learning experiment
Model comparison and deviance
Bibliographic note
Exercises
Missing-data imputation
Missing-data mechanisms
Missing-data methods that discard data
Simple missing-data approaches that retain all the data
Random imputation of a single variable
Imputation of several missing variables
Model-based imputation
Combining inferences from multiple imputations
Bibliographic note
Exercises
Appendixes
Six quick tips to improve your regression modeling
Fit many models
Do a little work to make your computations faster and more reliable
Graphing the relevant and not the irrelevant
Transformations
Consider all coefficients as potentially varying
Estimate causal inferences in a targeted way, not as a byproduct of a large regression
Statistical graphics for research and presentation
Reformulating a graph by focusing on comparisons
Scatterplots
Miscellaneous tips
Bibliographic note
Exercises
Software
Getting started with R, Bugs, and a text editor
Fitting classical and multilevel regressions in R
Fitting models in Bugs and R
Fitting multilevel models using R, Stata, SAS, and other software
Bibliographic note
References
Author index
Subject index

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