| |

| |

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 | |