
2025 Stata Conference • Nashville, TN • 31 July–01 August
Multilevel and Longitudinal Modeling Using Stata, Fourth EditionVolume I: Continuous ResponsesVolume II: Categorical Responses, Counts, and Survival |
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Comment from the Stata technical groupMultilevel and Longitudinal Modeling Using Stata, Fourth Edition, by Sophia Rabe-Hesketh and Anders Skrondal, is a complete resource for learning to model data in which observations are grouped—whether those groups are formed by a nesting structure, such as children nested in classrooms, or formed by repeated observations on the same individuals. This text introduces random-effects models, fixed-effects models, mixed-effects models, marginal models, dynamic models, and growth-curve models, all of which account for the grouped nature of these types of data. As Rabe-Hesketh and Skrondal introduce each model, they explain when the model is useful, its assumptions, how to fit and evaluate the model using Stata, and how to interpret the results. With this comprehensive coverage, researchers who need to apply multilevel models will find this book to be the perfect companion. It is also the ideal text for courses in multilevel modeling because it provides examples from a variety of disciplines as well as end-of-chapter exercises that allow students to practice newly learned material. The book comprises two volumes. Volume I focuses on linear models for continuous outcomes, while volume II focuses on generalized linear models for binary, ordinal, count, and other types of outcomes. Volume I begins with a review of linear regression and then builds on this review to introduce two-level models, the simplest extensions of linear regression to models for multilevel and longitudinal/panel data. Rabe-Hesketh and Skrondal introduce the random-intercept model without covariates, developing the model from principles and thereby familiarizing the reader with terminology, summarizing and relating the widely used estimating strategies, and providing historical perspective. Once the authors have established the foundation, they smoothly generalize to random-intercept models with covariates and then to a discussion of the various estimators (between, within, and random effects). The authors also discuss models with random coefficients. The text then turns to models specifically designed for longitudinal and panel data—dynamic models, marginal models, and growth-curve models. The last portion of volume I covers models with more than two levels and models with crossed random effects. The foundation and in-depth coverage of linear-model principles provided in volume I allow for a straightforward transition to generalized linear models for noncontinuous outcomes, which are described in volume II. This second volume begins with chapters introducing multilevel and longitudinal models for binary, ordinal, nominal, and count data. Focus then turns to survival analysis, introducing multilevel models for both discrete-time survival data and continuous-time survival data. The volume concludes by extending the two-level generalized linear models introduced in previous chapters to models with three or more levels and to models with crossed random effects. In both volumes, readers will find extensive applications of multilevel and longitudinal models. Using many datasets that appeal to a broad audience, Rabe-Hesketh and Skrondal provide worked examples in each chapter. They also show the breadth of Stata's commands for fitting the models discussed. They demonstrate Stata's xt suite of commands (xtreg, xtlogit, xtpoisson, etc.), which is designed for two-level random-intercept models for longitudinal/panel data. They demonstrate the me suite of commands (mixed, melogit, mepoisson, etc.), which is designed for multilevel models, including those with random coefficients and those with three or more levels. In volume 2, they discuss gllamm, a community-contributed Stata command developed by Rabe-Hesketh and Skrondal that can fit many latent-variable models, of which the generalized linear mixed-effects model is a special case.The types of models fit by the xt commands, the me commands, and gllamm sometimes overlap; when this happens, the authors highlight the differences in syntax, data organization, and output for the commands. The authors also point out the strengths and weaknesses of these commands, based on considerations such as computational speed, accuracy, available predictions, and available postestimation statistics. The fourth edition of Multilevel and Longitudinal Modeling Using Stata has been thoroughly revised and updated. In it, you will find new material on Kenward–Roger degrees-of-freedom adjustments for small sample sizes, difference-in-differences estimation for natural experiments, instrumental-variables estimation to account for level-one endogeneity, and Bayesian estimation for crossed-effects models. In addition, you will find new discussions of meologit, cmxtmixlogit, mestreg, menbreg, and other commands introduced in Stata since the third edition of the book. In summary, Multilevel and Longitudinal Modeling Using Stata, Fourth Edition is the most complete, up-to-date depiction of Stata’s capacity for fitting models to multilevel and longitudinal data. Readers will also find thorough explanations of the methods and practical advice for using these techniques. This text is a great introduction for researchers and students wanting to learn about these powerful data analysis tools. |
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About the authorSophia Rabe-Hesketh is a professor of educational statistics and biostatistics at the University of California, Berkeley. Anders Skrondal is a senior biostatistician at the Centre for Fertility and Health, Norwegian Institute of Public Health and an adjunct professor at the University of Oslo and at the University of California, Berkeley. |
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Table of contentsView table of contents >> List of tables
List of figures
List of displays
Preface (PDF)
Multilevel and longitudinal models: When and why?
I Preliminaries
1 Review of linear regression
1.1 Introduction
1.2 Is there gender discrimination in faculty salaries? 1.3 Independent-samples t test 1.4 One-way analysis of variance 1.5 Simple linear regression 1.6 Dummy variables 1.7 Multiple linear regression 1.8 Interactions 1.9 Dummy variables for more than two groups 1.10 Other types of interactions
1.10.1 Interaction between dummy variables
1.11 Nonlinear effects 1.10.2 Interaction between continuous covariates 1.12 Residual diagnostics 1.13 Causal and noncausal interpretations of regression coefficients
1.13.1 Regression as conditional expectation
1.14 Summary and further reading 1.13.2 Regression as structural model 1.15 Exercises II Two-level models
2 Variance-components models
2.1 Introduction
2.2 How reliable are peak-expiratory-flow measurements? 2.3 Inspecting within-subject dependence 2.4 The variance-components model
2.4.1 Model specification
2.5 Estimation using Stata 2.4.2 Path diagram 2.4.3 Between-subject heterogeneity 2.4.4 Within-subject dependence
Intraclass correlation
Intraclass correlation versus Pearson correlation
2.5.1 Data preparation: Reshaping from wide form to long form
2.6 Hypothesis tests and confidence intervals 2.5.2 Using xtreg 2.5.3 Using mixed
2.6.1 Hypothesis test and confidence interval for the population mean
2.7 Model as data-generating mechanism 2.6.2 Hypothesis test and confidence interval for the between-cluster variance
Likelihood-ratio test
Score test F test Confidence interval 2.8 Fixed versus random effects 2.9 Crossed versus nested effects 2.10 Parameter estimation
2.10.1 Model assumptions
2.11 Assigning values to the random intercepts
Mean structure and covariance structure
2.10.2 Different estimation methods Distributional assumptions 2.10.3 Inference for β
Estimate and standard error: Balanced case
Estimate: Unbalanced case
2.11.1 Maximum “likelihood” estimation
2.12 Summary and further reading
Implementation via OLS regression
2.11.2 Empirical Bayes prediction Implementation via the mean total residual 2.11.3 Empirical Bayes standard errors
Posterior and comparative standard errors
2.11.4 Bayesian interpretation of REML estimation and prediction Diagnostic standard errors Accounting for uncertainty in ˆβ 2.13 Exercises 3 Random-intercept models with covariates
3.1 Introduction
3.2 Does smoking during pregnancy affect birthweight?
3.2.1 Data structure and descriptive statistics
3.3 The linear random-intercept model with covariates
3.3.1 Model specification
3.4 Estimation using Stata 3.3.2 Model assumptions 3.3.3 Mean structure 3.3.4 Residual covariance structure 3.3.5 Graphical illustration of random-intercept model
3.4.1 Using xtreg
3.5 Coefficients of determination or variance explained 3.4.2 Using mixed 3.6 Hypothesis tests and confidence intervals
3.6.1 Hypothesis tests for individual regression coefficients
3.7 Between and within effects of level-1 covariates 3.6.2 Joint hypothesis tests for several regression coefficients 3.6.3 Predicted means and confidence intervals 3.6.4 Hypothesis test for random-intercept variance
3.7.1 Between-mother effects
3.8 Fixed versus random effects revisited 3.7.2 Within-mother effects 3.7.3 Relations among estimators 3.7.4 Level-2 endogeneity and cluster-level confounding 3.7.5 Allowing for different within and between effects 3.7.6 Robust Hausman test 3.9 Assigning values to random effects: Residual diagnostics 3.10 More on statistical inference
3.10.1 Overview of estimation methods
3.11 Summary and further reading
Pooled OLS
3.10.2 Consequences of using standard regression modeling for clustered data Feasible generalized least squares (FGLS) ML by iterative GLS (IGLS) ML by Newton–Raphson and Fisher scoring ML by the expectation-maximization (EM) algorithm REML
Purely between-cluster covariate
3.10.3 Power and sample-size determination Purely within-cluster covariate
Purely between-cluster covariate
Purely within-cluster covariate 3.12 Exercises 4 Random-coefficient models
4.1 Introduction
4.2 How effective are different schools? 4.3 Separate linear regressions for each school 4.4 Specification and interpretation of a random-coefficient model
4.4.1 Specification of a random-coefficient model
4.5 Estimation using mixed 4.4.2 Interpretation of the random-effects variances and covariances
4.5.1 Random-intercept model
4.6 Testing the slope variance 4.5.2 Random-coefficient model 4.7 Interpretation of estimates 4.8 Assigning values to the random intercepts and slopes
4.8.1 Maximum “likelihood” estimation
4.9 Two-stage model formulation 4.8.2 Empirical Bayes prediction 4.8.3 Model visualization 4.8.4 Residual diagnostics 4.8.5 Inferences for individual schools 4.10 Some warnings about random-coefficient models
4.10.1 Meaningful specification
4.11 Summary and further reading 4.10.2 Many random coefficients 4.10.3 Convergence problems 4.10.4 Lack of identification 4.12 Exercises III Models for longitudinal and panel data
Introduction to models for longitudinal and panel data (part III)
5 Subject-specific effects and dynamic models
5.1 Introduction
5.2 Random-effects approach: No endogeneity 5.3 Fixed-effects approach: Level-2 endogeneity
5.3.1 De-meaning and subject dummies
5.4 Difference-in-differences and repeated-measures ANOVA
De-meaning
5.3.2 Hausman test Subject dummies 5.3.3 Mundlak approach and robust Hausman test 5.3.4 First-differencing
5.4.1 Does raising the minimum wage reduce employment?
5.5 Subject-specific coefficients 5.4.2 Repeated-measures ANOVA
5.5.1 Random-coefficient model: No endogeneity
5.6 Hausman–Taylor: Level-2 endogeneity for level-1 and level-2 covariates 5.5.2 Fixed-coefficient model: Level-2 endogeneity 5.7 Instrumental-variable methods: Level-1 (and level-2) endogeneity
5.7.1 Do deterrents decrease crime rates?
5.8 Dynamic models 5.7.2 Conventional fixed-effects approach 5.7.3 Fixed-effects IV estimator 5.7.4 Random-effects IV estimator 5.7.5 More Hausman tests
5.8.1 Dynamic model without subject-specific intercepts
5.9 Missing data and dropout 5.8.2 Dynamic model with subject-specific intercepts
5.9.1 Maximum likelihood estimation under MAR: A simulation
5.9 Summary and further reading 5.10 Exercises 6 Marginal models
6.1 Introduction
6.2 Mean structure 6.3 Covariance structures
6.3.1 Unstructured covariance matrix
6.4 Hybrid and complex marginal models 6.3.2 Random-intercept or compound symmetric/exchangeable structure 6.3.3 Random-coefficient structure 6.3.4 Autoregressive and exponential structures 6.3.5 Moving-average residual structure 6.3.6 Banded and Toeplitz structures
6.4.1 Random effects and correlated level-1 residuals
6.5 Comparing the fit of marginal models 6.4.2 Heteroskedastic level-1 residuals over occasions 6.4.3 Heteroskedastic level-1 residuals over groups 6.4.4 Different covariance matrices over groups 6.6 Generalized estimating equations (GEE) 6.7 Marginal modeling with few units and many occasions
6.7.1 Is a highly organized labor market beneficial for economic growth?
6.8 Summary and further reading 6.7.2 Marginal modeling for long panels 6.7.3 Fitting marginal models for long panels in Stata 6.9 Exercises 7 Growth-curve models
7.1 Introduction
7.2 How do children grow?
7.2.1 Observed growth trajectories
7.3 Models for nonlinear growth
7.3.1 Polynomial models
7.4 Two-stage model formulation and cross-level interaction
Estimation using mixed
7.3.2 Piecewise linear models Predicting the mean trajectory Predicting trajectories for individual children
Estimation using mixed
Predicting the mean trajectory 7.5 Heteroskedasticity
7.5.1 Heteroskedasticity at level 1
7.6 How does reading improve from kindergarten through third grade? 7.5.2 Heteroskedasticity at level 2 7.7 Growth-curve model as a structural equation model
7.7.1 Estimation using sem
7.8 Summary and further reading 7.7.2 Estimation using mixed 7.9 Exercises IV Models with nested and crossed random effects
8 Higher-level models with nested random effects
8.1 Introduction
8.2 Do peak-expiratory-flow measurements vary between methods within subjects? 8.3 Inspecting sources of variability 8.4 Three-level variance-components models 8.5 Different types of intraclass correlation 8.6 Estimation using mixed 8.7 Empirical Bayes prediction 8.8 Testing variance components 8.9 Crossed versus nested random effects revisited 8.10 Does nutrition affect cognitive development of Kenyan children? 8.11 Describing and plotting three-level data
8.11.1 Data structure and missing data
8.12 Three-level random-intercept model 8.11.2 Level-1 variables 8.11.3 Level-2 variables 8.11.4 Level-3 variables 8.11.5 Plotting growth trajectories
8.12.1 Model specification: Reduced form
8.13 Three-level random-coefficient models 8.12.2 Model specification: Three-stage formulation 8.12.3 Estimation using mixed
8.13.1 Random coefficient at the child level
8.14 Residual diagnostics and predictions
Estimation using mixed
8.13.2 Random coefficient at the child and school levels
Estimation using mixed
8.15 Summary and further reading 8.16 Exercises 9 Crossed random effects
9.1 Introduction
9.2 How does investment depend on expected profit and capital stock? 9.3 A two-way error-components model
9.3.1 Model specification
9.4 How much do primary and secondary schools affect attainment at age 16? 9.3.2 Residual variances, covariances, and intraclass correlations
Longitudinal correlations
9.3.3 Estimation using mixed Cross-sectional correlations 9.3.4 Prediction 9.5 Data structure 9.6 Additive crossed random-effects model
9.6.1 Specification
9.7 Crossed random-effects model with random interaction 9.6.2 Intraclass correlations 9.6.3 Estimation using mixed
9.7.1 Model specification
9.8 A trick requiring fewer random effects 9.7.2 Intraclass correlations 9.7.3 Estimation using mixed 9.7.4 Testing variance components 9.7.5 Some diagnostics 9.9 Summary and further reading 9.10 Exercises A Useful Stata commands
References
Author index (PDF)
Subject index (PDF)
List of tables
List of figures
List of displays
V Models for categorical responses
10 Dichotomous or binary responses (PDF)
10.1 Introduction
10.2 Single-level logit and probit regression models for dichotomous responses
10.2.1 Generalized linear model formulation
10.3 Which treatment is best for toenail infection?
Labor-participation data
10.2.2 Latent-response formulation Estimation using logit Estimation using glm
Logistic regression
Probit regression Estimation using probit 10.4 Longitudinal data structure 10.5 Proportions and fitted population-averaged or marginal probabilities
Estimation using logit
10.6 Random-intercept logistic regression
10.6.1 Model specification
10.7 Subject-specific or conditional versus population-averaged or marginal relationships
Reduced-form specification
10.6.2 Model assumptions Two-stage formulation 10.6.3 Estimation
Using xtlogit
Using melogit Using gllamm 10.8 Measures of dependence and heterogeneity
10.8.1 Conditional or residual intraclass correlation of the latent responses
10.9 Inference for random-intercept logistic models 10.8.2 Median odds ratio 10.8.3 Measures of association for observed responses at median fixed part of the model
10.9.1 Tests and confidence intervals for odds ratios
10.10 Maximum likelihood estimation 10.9.2 Tests of variance components
10.10.1 Adaptive quadrature
10.11 Assigning values to random effects 10.10.2 Some speed and accuracy considerations
Integration methods and number of quadrature points
Starting values Using melogit and gllamm for collapsible data Spherical quadrature in gllamm
10.11.1 Maximum “likelihood” estimation
10.12 Different kinds of predicted probabilities 10.11.2 Empirical Bayes prediction 10.11.3 Empirical Bayes modal prediction
10.12.1 Predicted population-averaged or marginal probabilities
10.13 Other approaches to clustered dichotomous data 10.12.2 Predicted subject-specific probabilities
Predictions for hypothetical subjects: Conditional probabilities
Predictions for the subjects in the sample: Posterior mean probabilities
10.13.1 Conditional logistic regression
10.14 Summary and further reading
Estimation using clogit
10.13.2 Generalized estimating equations (GEE)
Estimation using xtgee
10.15 Exercises 11 Ordinal responses
11.1 Introduction
11.2 Single-level cumulative models for ordinal responses
11.2.1 Generalized linear model formulation
11.3 Are antipsychotic drugs effective for patients with schizophrenia? 11.2.2 Latent-response formulation 11.2.3 Proportional odds 11.2.4 Identification 11.4 Longitudinal data structure and graphs
11.4.1 Longitudinal data structure
11.5 Single-level proportional-odds model 11.4.2 Plotting cumulative proportions 11.4.3 Plotting cumulative sample logits and transforming the time scale
11.5.1 Model specification
11.6 Random-intercept proportional-odds model
Estimation using ologit
11.6.1 Model specification
11.7 Random-coefficient proportional-odds model
Estimation using meologit
11.6.2 Measures of dependence and heterogeneity Estimation using gllamm
Residual intraclass correlation of latent responses
Median odds ratio
11.7.1 Model specification
11.8 Different kinds of predicted probabilities
Estimation using meologit
Estimation using gllamm
11.8.1 Predicted population-averaged or marginal probabilities
11.9 Do experts differ in their grading of student essays? 11.8.2 Predicted subject-specific probabilities: Posterior mean 11.10 A random-intercept probit model with grader bias
11.10.1 Model specification
11.11 Including grader-specific measurement-error variances
Estimation using gllamm
11.11.1 Model specification
11.12 Including grader-specific thresholds
Estimation using gllamm
11.12.1 Model specification
11.13 Other link functions
Estimation using gllamm
Cumulative complementary log–log model
Continuation-ratio logit model Adjacent-category logit model Baseline-category logit and stereotype models 11.15 Exercises 12 Nominal responses and discrete choice
12.1 Introduction
12.2 Single-level models for nominal responses
12.2.1 Multinomial logit models
12.3 Independence from irrelevant alternatives
Transport data version 1
12.2.2 Conditional logit models with alternative-specific covariates Estimation using mlogit
Transport data version 2: Expanded form
12.2.3 Conditional logit models with alternative- and unit-specific covariates Estimation using clogit Estimation using cmclogit
Estimation using clogit
Estimation using cmclogit 12.4 Utility-maximization formulation 12.5 Does marketing affect choice of yogurt? 12.6 Single-level conditional logit models
12.6.1 Conditional logit models with alternative-specific intercepts
12.7 Multilevel conditional logit models
Estimation using clogit
Estimation using cmclogit
12.7.1 Preference heterogeneity: Brand-specific random intercepts
12.8 Prediction of marginal choice probabilities
Estimation using cmxtmixlogit
12.7.2 Response heterogeneity: Marketing variables with random coefficients Estimation using gllamm
Estimation using cmxtmixlogit
12.7.3 Preference and response heterogeneity Estimation using gllamm
Estimation using cmxtmixlogit
Estimation using gllamm 12.9 Prediction of random effects and household-specific choice probabilities 12.10 Summary and further reading 12.11 Exercises VI Models for counts
13 Counts
13.1 Introduction
13.2 What are counts?
13.2.1 Counts versus proportions
13.3 Single-level Poisson models for counts 13.2.2 Counts as aggregated event-history data 13.4 Did the German healthcare reform reduce the number of doctor visits? 13.5 Longitudinal data structure 13.6 Single-level Poisson regression
13.6.1 Model specification
13.7 Random-intercept Poisson regression
Estimation using poisson
Estimation using glm
13.7.1 Model specification
13.8 Random-coefficient Poisson regression 13.7.2 Measures of dependence and heterogeneity 13.7.3 Estimation
Using xtpoisson
Using mepoisson Using gllamm
13.8.1 Model specification
13.9 Overdispersion in single-level models
Estimation using mepoisson
Estimation using gllamm
13.9.1 Normally distributed random intercept
13.10 Level-1 overdispersion in two-level models
Estimation using xtpoisson
13.9.2 Negative binomial models
Mean dispersion or NB2
13.9.3 Quasilikelihood Constant dispersion or NB1
Estimation using glm
13.10.1 Random-intercept Poisson model with robust standard errors
13.11 Other approaches to two-level count data
Estimation using mepoisson
13.10.2 Three-level random-intercept model 13.10.3 Negative binomial models with random intercepts
Estimation using menbreg
13.10.4 The HHG model
13.11.1 Conditional Poisson regression
13.12 Marginal and conditional effects when responses are MAR
Estimation using xtpoisson, fe
13.11.2 Conditional negative binomial regression Estimation using Poisson regression with dummy variables for clusters 13.11.3 Generalized estimating equations
Estimation using xtgee
Simulation
13.13 Which Scottish counties have a high risk of lip cancer? 13.14 Standardized mortality ratios 13.15 Random-intercept Poisson regression
13.15.1 Model specification
13.16 Nonparametric maximum likelihood estimation
Estimation using gllamm
13.15.2 Prediction of standardized mortality ratios
13.16.1 Specification
13.17 Summary and further reading
Estimation using gllamm
13.16.2 Prediction 13.18 Exercises VII Models for survival or duration data
Introduction to models for survival or duration data (part VII)
14 Discrete-time survival
14.1 Introduction
14.2 Single-level models for discrete-time survival data
14.2.1 Discrete-time hazard and discrete-time survival
14.3 How does mother's birth history affect child mortality?
Promotions data
14.2.2 Data expansion for discrete-time survival analysis 14.2.3 Estimation via regression models for dichotomous responses
Estimation using logit
14.2.4 Including time-constant covariates
Estimation using logit
14.2.5 Including time-varying covariates
Estimation using logit
14.2.6 Multiple absorbing events and competing risks
Estimation using mlogit
14.2.7 Handling left-truncated data 14.4 Data expansion 14.5 Proportional hazards and interval-censoring 14.6 Complementary log–log models
14.6.1 Marginal baseline hazard
14.7 Random-intercept complementary log-log model
Estimation using cloglog
14.6.2 Including covariates
Estimation using cloglog
14.7.1 Model specification
Estimation using mecloglog
14.8 Population-averaged or marginal vs. cluster-specific or conditional
survival probabilities 14.9 Summary and further reading 14.10 Exercises 15 Continuous-time survival
15.1 Introduction
15.2 What makes marriages fail? 15.3 Hazards and survival 15.4 Proportional hazards models
15.4.1 Piecewise exponential model
15.5 Accelerated failure-time models
Estimation using streg
15.4.2 Cox regression model Estimation using poisson
Estimation using stcox
15.4.3 Cox regression via Poisson regression for expanded data
Estimation using xtpoisson, fe
15.4.4 Approximate Cox regression: Poisson regression, smooth baseline hazard
Estimation using poisson
15.5.1 Log-normal model
15.6 Time-varying covariates
Estimation using streg
Estimation using stintreg
Estimation using streg
15.7 Does nitrate reduce the risk of angina pectoris? 15.8 Marginal modeling
15.8.1 Cox regression with occasion-specific dummy variables
15.9 Multilevel proportional hazards models
Estimation using stcox
15.8.2 Cox regression with occasion-specific baseline hazards
Estimation using stcox, strata
15.8.3 Approximate Cox regression
Estimation using poisson
15.9.1 Cox regression with gamma shared frailty
15.10 Multilevel accelerated failure-time models
Estimation using stcox, shared
15.9.2 Approximate Cox regression with log-normal shared frailty
Estimation using mepoisson
15.9.3 Approximate Cox regression with normal random intercept and coefficient
Estimation using mepoisson
15.10.1 Log-normal model with gamma shared frailty
15.11 Fixed-effects approach
Estimation using streg
15.10.2 Log-normal model with log-normal shared frailty
Estimation using mestreg
15.10.3 Log-normal model with normal random intercept and random coefficient
Estimation using mestreg
15.11.1 Stratified Cox regression with subject-specific baseline hazards
15.12 Different approaches to recurrent-event data
Estimation using stcox, strata
15.12.1 Total time risk interval
15.13 Summary and further reading 15.12.2 Counting process risk interval 15.12.3 Gap-time risk interval 15.14 Exercises VIII Models with nested and crossed random effects
16 Models with nested and crossed random effects
16.1 Introduction
16.2 Did the Guatemalan-immunization campaign work? 16.3 A three-level random-intercept logistic regression model
16.3.1 Model specification
16.4 A three-level random-coefficient logistic regression model 16.3.2 Measures of dependence and heterogeneity
Types of residual intraclass correlations of the latent responses
16.3.3 Three-stage formulation Types of median odds ratios 16.3.4 Estimation
Using melogit
Using gllamm
16.4.1 Estimation
16.5 Prediction of random effects
Using melogit
Using gllamm
16.5.1 Empirical Bayes prediction
16.6 Different kinds of predicted probabilities 16.5.2 Empirical Bayes modal prediction
16.6.1 Predicted population-averaged or marginal probabilities: New clusters
16.7 Do salamanders from different populations mate successfully 16.6.2 Predicted median or conditional probabilities 16.6.3 Predicted posterior mean probabilities: Existing clusters 16.8 Crossed random-effects logistic regression
16.8.1 Setup for estimating crossed random-effects model using melogit
16.9 Summary and further reading 16.8.2 Approximate maximum likelihood estimation
Estimation using melogit
16.8.3 Bayesian estimation
Brief introduction to Bayesian inference
16.8.4 Estimates compared Priors for the salamander data Estimation using bayes: melogit 16.8.5 Fully Bayesian versus empirical Bayesian inference for random effects 16.10 Exercises A Syntax for gllamm, eq, and gllapred: The bare essentials
B Syntax for gllamm
C Syntax for gllapred
D Syntax for gllasim
References
Author index (PDF)
Subject index (PDF)
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