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书籍名称:Multilevel and Longitudinal Modeling Using Stata, Third Edition
出版社:Stata Press
作者: Sophia Rabe-Hesketh and Anders Skrondal
语种: 英文
页数: 974
开本: 胶版纸
纸张:974 I S B N: 978-1-59718-108-2
装订: 平装


List of Tables List of Figures Preface 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 1.10.2 Interaction between continuous covariates 1.11 Nonlinear effects 1.12 Residual diagnostics 1.13 Causal and noncausal interpretations of regression coefficients 1.13.1 Regression as conditional expectation 1.13.2 Regression as structural model 1.14 Summary and further reading 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 2.4.2 Path diagram 2.4.3 Between-subject heterogeneity 2.4.4 Within-subject dependence Intraclass correlation Intraclass correlation versus Pearson correlation 2.5 Estimation using Stata 2.5.1 Data preparation: Reshaping to long form 2.5.2 Using xtreg 2.5.3 Using xtmixed 2.6 Hypothesis tests and confidence intervals 2.6.1 Hypothesis test and confidence interval for the population mean 2.6.2 Hypothesis test and confidence interval for the between-cluster variance Likelihood-ratio test F test Confidence intervals 2.7 Model as data-generating mechanism 2.8 Fixed versus random effects 2.9 Crossed versus nested effects 2.10 Parameter estimation 2.10.1 Model assumptions Mean structure and covariance structure Distributional assumptions 2.10.2 Different estimation methods 2.10.3 Inference for β Estimate and standard error: Balanced case Estimate: Unbalanced case 2.11 Assigning values to the random intercepts 2.11.1 Maximum “likelihood” estimation Implementation via OLS regression Implementation via the mean total residual 2.11.2 Empirical Bayes prediction 2.11.3 Empirical Bayes standard errors Comparative standard errors Diagnostic standard errors 2.12 Summary and further reading 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 3.3.2 Model assumptions 3.3.3 Mean structure 3.3.4 Residual variance and intraclass correlation 3.3.5 Graphical illustration of random-intercept model 3.4 Estimation using Stata 3.4.1 Using xtreg 3.4.2 Using xtmixed 3.5 Coefficients of determination or variance explained 3.6 Hypothesis tests and confidence intervals 3.6.1 Hypothesis tests for regression coefficients Hypothesis tests for individual regression coefficients Joint hypothesis tests for several regression coefficients 3.6.2 Predicted means and confidence intervals 3.6.3 Hypothesis test for random-intercept variance 3.7 Between and within effects of level-1 covariates 3.7.1 Between-mother effects 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 Hausman endogeneity test 3.8 Fixed versus random effects revisited 3.9 Assigning values to random effects: Residual diagnostics 3.10 More on statistical inference 3.10.1 Overview of estimation methods 3.10.2 Consequences of using standard regression modeling for clustered data 3.10.3 Power and sample-size determination 3.11 Summary and further reading 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 4.4.2 Interpretation of the random-effects variances and covariances 4.5 Estimation using xtmixed 4.5.1 Random-intercept model 4.5.2 Random-coefficient model 4.6 Testing the slope variance 4.7 Interpretation of estimates 4.8 Assigning values to the random intercepts and slopes 4.8.1 Maximum “likelihood” estimation 4.8.2 Empirical Bayes prediction 4.8.3 Model visualization 4.8.4 Residual diagnostics 4.8.5 Inferences for individual schools 4.9 Two-stage model formulation 4.10 Some warnings about random-coefficient models 4.10.1 Meaningful specification 4.10.2 Many random coefficients 4.10.3 Convergence problems 4.10.4 Lack of identification 4.11 Summary and further reading 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 Conventional random-intercept model 5.3 Random-intercept models accommodating endogenous covariates 5.3.1 Consistent estimation of effects of endogenous time-varying covariates 5.3.2 Consistent estimation of effects of endogenous time-varying and endogenous time-constant covariates 5.4 Fixed-intercept model 5.4.1 Using xtreg or regress with a differencing operator 5.4.2 Using anova 5.5 Random-coefficient model 5.6 Fixed-coefficient model 5.7 Lagged-response or dynamic models 5.7.1 Conventional lagged-response model 5.7.2 Lagged-response model with subject-specific intercepts 5.8 Missing data and dropout 5.8.1 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 6.3.2 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 Hybrid and complex marginal models 6.4.1 Random effects and correlated level-1 residuals 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 6.5 Comparing the fit of marginal models 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? 6.7.2 Marginal modeling for long panels 6.7.3 Fitting marginal models for long panels in Stata 6.8 Summary and further reading 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 Fitting the models Predicting the mean trajectory Predicting trajectories for individual children 7.3.2 Piecewise linear models Fitting the models Predicting the mean trajectory 7.4 Two-stage model formulation 7.5 Heteroskedasticity 7.5.1 Heteroskedasticity at level 1 7.5.2 Heteroskedasticity at level 2 7.6 How does reading improve from kindergarten through third grade? 7.7 Growth-curve model as a structural equation model 7.7.1 Estimation using sem 7.7.2 Estimation using xtmixed 7.8 Summary and further reading 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 xtmixed 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 8.11.2 Level-1 variables 8.11.3 Level-2 variables 8.11.4 Level-3 variables 8.11.5 Plotting growth trajectories 8.12 Three-level random-intercept model 8.12.1 Model specification: Reduced form 8.12.2 Model specification: Three-stage formulation 8.12.3 Estimation using xtmixed 8.13 Three-level random-coefficient models 8.13.1 Random coefficient at the child level 8.13.2 Random coefficient at the child and school levels 8.14 Residual diagnostics and predictions 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 9.3.2 Residual variances, covariances, and intraclass correlations Longitudinal correlations Cross-sectional correlations 9.3.3 Estimation using xtmixed 9.3.4 Prediction 9.4 How much do primary and secondary schools affect attainment at age 16? 9.5 Data structure 9.6 Additive crossed random-effects model 9.6.1 Specification 9.6.2 Estimation using xtmixed 9.7 Crossed random-effects model with random interaction 9.7.1 Model specification 9.7.2 Intraclass correlations 9.7.3 Estimation using xtmixed 9.7.4 Testing variance components 9.7.5 Some diagnostics 9.8 A trick requiring fewer random effects 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 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 10.2.2 Latent-response formulation Logistic regression Probit regression 10.3 Which treatment is best for toenail infection? 10.4 Longitudinal data structure 10.5 Proportions and fitted population-averaged or marginal probabilities 10.6 Random-intercept logistic regression 10.6.1 Model specification Reduced-form specification Two-stage formulation 10.7 Estimation of random-intercept logistic models 10.7.1 Using xtlogit 10.7.2 Using xtmelogit 10.7.3 Using gllamm 10.8 Subject-specific or conditional vs. population-averaged or marginal relationships 10.9 Measures of dependence and heterogeneity 10.9.1 Conditional or residual intraclass correlation of the latent responses 10.9.2 Median odds ratio 10.9.3 Measures of association for observed responses at median fixed part of the model 10.10 Inference for random-intercept logistic models 10.10.1 Tests and confidence intervals for odds ratios 10.10.2 Tests of variance components 10.11 Maximum likelihood estimation 10.11.1 Adaptive quadrature 10.11.2 Some speed and accuracy considerations Advice for speeding up estimation in gllamm 10.12 Assigning values to random effects 10.12.1 Maximum “likelihood” estimation 10.12.2 Empirical Bayes prediction 10.12.3 Empirical Bayes modal prediction 10.13 Different kinds of predicted probabilities 10.13.1 Predicted population-averaged or marginal probabilities 10.13.2 Predicted subject-specific probabilities Predictions for hypothetical subjects: Conditional probabilities Predictions for the subjects in the sample: Posterior mean probabilities 10.14 Other approaches to clustered dichotomous data 10.14.1 Conditional logistic regression 10.14.2 Generalized estimating equations (GEE) 10.15 Summary and further reading 10.16 Exercises 11 Ordinal responses 11.1 Introduction 11.2 Single-level cumulative models for ordinal responses 11.2.1 Generalized linear model formulation 11.2.2 Latent-response formulation 11.2.3 Proportional odds 11.2.4 Identification 11.3 Are antipsychotic drugs effective for patients with schizophrenia? 11.4 Longitudinal data structure and graphs 11.4.1 Longitudinal data structure 11.4.2 Plotting cumulative proportions 11.4.3 Plotting cumulative sample logits and transforming the time scale 11.5 A single-level proportional odds model 11.5.1 Model specification 11.5.2 Estimation using Stata 11.6 A random-intercept proportional odds model 11.6.1 Model specification 11.6.2 Estimation using Stata 11.6.3 Measures of dependence and heterogeneity Residual intraclass correlation of latent responses Median odds ratio 11.7 A random-coefficient proportional odds model 11.7.1 Model specification 11.7.2 Estimation using gllamm 11.8 Different kinds of predicted probabilities 11.8.1 Predicted population-averaged or marginal probabilities 11.8.2 Predicted subject-specific probabilities: Posterior mean 11.9 Do experts differ in their grading of student essays? 11.10 A random-intercept probit model with grader bias 11.10.1 Model specification 11.10.2 Estimation using gllamm 11.11 Including grader-specific measurement error variances 11.11.1 Model specification 11.11.2 Estimation using gllamm 11.12 Including grader-specific thresholds 11.12.1 Model specification 11.12.2 Estimation using gllamm 11.13 Other link functions Cumulative complementary log-log model Continuation-ratio logit model Adjacent-category logit model Baseline-category logit and stereotype models 11.14 Summary and further reading 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 12.2.2 Conditional logit models Classical conditional logit models Conditional logit models also including covariates that vary only over units 12.3 Independence from irrelevant alternatives 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 12.7.1 Preference heterogeneity: Brand-specific random intercepts 12.7.2 Response heterogeneity: Marketing variables with random coefficients 12.7.3 Preference and response heterogeneity Estimation using gllamm Estimation using mixlogit 12.8 Prediction of random effects and response probabilities 12.9 Summary and further reading 12.10 Exercises VI Models for counts 13 Counts 13.1 Introduction 13.2 What are counts? 13.2.1 Counts versus proportions 13.2.2 Counts as aggregated event-history data 13.3 Single-level Poisson models for counts 13.4 Did the German health-care reform reduce the number of doctor visits? 13.5 Longitudinal data structure 13.6 Single-level Poisson regression 13.6.1 Model specification 13.6.2 Estimation using Stata 13.7 Random-intercept Poisson regression 13.7.1 Model specification 13.7.2 Measures of dependence and heterogeneity 13.7.3 Estimation using Stata Using xtpoisson Using xtmepoisson Using gllamm 13.8 Random-coefficient Poisson regression 13.8.1 Model specification 13.8.2 Estimation using Stata Using xtmepoisson Using gllamm 13.8.3 Interpretation of estimates 13.9 Overdispersion in single-level models 13.9.1 Normally distributed random intercept 13.9.2 Negative binomial models Mean dispersion or NB2 Constant dispersion or NB1 13.9.3 Quasilikelihood 13.10 Level-1 overdispersion in two-level models 13.11 Other approaches to two-level count data 13.11.1 Conditional Poisson regression 13.11.2 Conditional negative binomial regression 13.11.3 Generalized estimating equations 13.12 Marginal and conditional effects when responses are MAR 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 13.15.2 Estimation using gllamm 13.15.3 Prediction of standardized mortality ratios 13.16 Nonparametric maximum likelihood estimation 13.16.1 Specification 13.16.2 Estimation using gllamm 13.16.3 Prediction 13.17 Summary and further reading 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 14.2.2 Data expansion for discrete-time survival analysis 14.2.3 Estimation via regression models for dichotomous responses 14.2.4 Including covariates Time-constant covariates Time-varying covariates 14.2.5 Multiple absorbing events and competing risks 14.2.6 Handling left-truncated data 14.3 How does birth history affect child mortality? 14.4 Data expansion 14.5 Proportional hazards and interval-censoring 14.6 Complementary log-log models 14.7 A random-intercept complementary log-log model 14.7.1 Model specification 14.7.2 Estimation using Stata 14.8 Population-averaged or marginal vs. subject-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 15.4.2 Cox regression model 15.4.3 Poisson regression with smooth baseline hazard 15.5 Accelerated failure-time models 15.5.1 Log-normal model 15.6 Time-varying covariates 15.7 Does nitrate reduce the risk of angina pectoris? 15.8 Marginal modeling 15.8.1 Cox regression 15.8.2 Poisson regression with smooth baseline hazard 15.9 Multilevel proportional hazards models 15.9.1 Cox regression with gamma shared frailty 15.9.2 Poisson regression with normal random intercepts 15.9.3 Poisson regression with normal random intercept and random coefficient 15.10 Multilevel accelerated failure-time models 15.10.1 Log-normal model with gamma shared frailty 15.10.2 Log-normal model with log-normal shared frailty 15.11 A fixed-effects approach 15.11.1 Cox regression with subject-specific baseline hazards 15.12 Different approaches to recurrent-event data 15.12.1 Total time 15.12.2 Counting process 15.12.3 Gap time 15.13 Summary and further reading 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 16.3.2 Measures of dependence and heterogeneity Types of residual intraclass correlations of the latent responses Types of median odds ratios 16.3.3 Three-stage formulation 16.4 Estimation of three-level random-intercept logistic regression models 16.4.1 Using gllamm 16.4.2 Using xtmelogit 16.5 A three-level random-coefficient logistic regression model 16.6 Estimation of three-level random-coefficient logistic regression models 16.6.1 Using gllamm 16.6.2 Using xtmelogit 16.7 Prediction of random effects 16.7.1 Empirical Bayes prediction 16.7.2 Empirical Bayes modal prediction 16.8 Different kinds of predicted probabilities 16.8.1 Predicted population-averaged or marginal probabilities: New clusters 16.8.2 Predicted median or conditional probabilities 16.8.3 Predicted posterior mean probabilities: Existing clusters 16.9 Do salamanders from different populations mate successfully? 16.10 Crossed random-effects logistic regression 16.11 Summary and further reading 16.12 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)


    Generalized linear models (GLMs) extend linear regression to models with a non-Gaussian or even discrete response. GLM theory is predicated on the exponential family of distributions—a class so rich that it includes the commonly used logit, probit, and Poisson models. Although one can fit these models in Stata by using specialized commands (for example, logit for logit models), fitting them as GLMs with Stata’s glm command offers some advantages. For example, model diagnostics may be calculated and interpreted similarly regardless of the assumed distribution.
    This text thoroughly covers GLMs, both theoretically and computationally, with an emphasis on Stata. The theory consists of showing how the various GLMs are special cases of the exponential family, showing general properties of this family of distributions, and showing the derivation of maximum likelihood (ML) estimators and standard errors. Hardin and Hilbe show how iteratively reweighted least squares, another method of parameter estimation, is a consequence of ML estimation using Fisher scoring. The authors also discuss different methods of estimating standard errors, including robust methods, robust methods with clustering, Newey–West, outer product of the gradient, bootstrap, and jackknife. The thorough coverage of model diagnostics includes measures of influence such as Cook’s distance, several forms of residuals, the Akaike and Bayesian information criteria, and various R2-type measures of explained variability.
    After presenting general theory, Hardin and Hilbe then break down each distribution. Each distribution has its own chapter that explains the computational details of applying the general theory to that particular distribution. Pseudocode plays a valuable role here because it lets the authors describe computational algorithms relatively simply. Devoting an entire chapter to each distribution (or family, in GLM terms) also allows for the inclusion of real-data examples showing how Stata fits such models, as well as the presentation of certain diagnostics and analytical strategies that are unique to that family. The chapters on binary data and on count (Poisson) data are excellent in this regard. Hardin and Hilbe give ample attention to the problems of overdispersion and zero inflation in count-data models.
    The final part of the text concerns extensions of GLMs. First, the authors cover multinomial responses, both ordered and unordered. Although multinomial responses are not strictly a part of GLM, the theory is similar in that one can think of a multinomial response as an extension of a binary response. The examples presented in these chapters often use the authors’ own Stata programs, augmenting official Stata’s capabilities. Second, GLMs may be extended to clustered data through generalized estimating equations (GEEs), and one chapter covers GEE theory and examples. GLMs may also be extended by programming one’s own family and link functions for use with Stata’s official glm command, and the authors detail this process. Finally, the authors describe extensions for multivariate models and Bayesian analysis.
    The fourth edition includes two new chapters. The first introduces bivariate and multivariate models for binary and count outcomes. The second covers Bayesian analysis and demonstrates how to use the bayes: prefix and the bayesmh command to fit Bayesian models for many of the GLMs that were discussed in previous chapters. Additionally, the authors added discussions of the generalized negative binomial models of Waring and Famoye. New explanations of working with heaped data, clustered data, and bias-corrected GLMs are included. The new edition also incorporates more examples of creating synthetic data for models such as Poisson, negative binomial, hurdle, and finite mixture models.