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