Multilevel and Longitudinal Modeling Using Stata Volume II: Categorical Responses, Counts, and Survival

Volume II is devoted to generalized linear mixed models for binary, categorical, count, and survival outcomes. The second volume has seven chapters also organized into four parts. The first three parts in volume II cover models for categorical responses, including binary, ordinal, and nominal (a new chapter); models for count data; and models for survival data, including discrete-time and continuous-time (a new chapter) survival responses. The fourth and final part in volume II describes models with nested and crossed-random effects with an emphasis on binary outcomes.

 

The book has extensive applications of generalized mixed models performed in Stata. Rabe-Hesketh and Skrondal developed gllamm, a Stata program that can fit many latent-variable models, of which the generalized linear mixed model is a special case. As of version 10, Stata contains the xtmixed,xtmelogit, and xtmepoisson commands for fitting multilevel models, in addition to other xt commands for fitting standard random-intercept models. The types of models fit by these commands sometimes overlap; when this happens, the authors highlight the differences in syntax, data organization, and output for the two (or more) commands that can be used to fit the same model. The authors also point out the relative strengths and weaknesses of each command when used to fit the same model, based on considerations such as computational speed, accuracy, available predictions, and available postestimation statistics.

 

In summary, this book is the most complete, up-to-date depiction of Stata’s capacity for fitting generalized linear mixed models. The authors provide an ideal introduction for Stata users wishing to learn about this powerful data analysis tool.

List of Tables
List of Figures

 

V Models for categorical responses

 

10. DICHOTOMOUS OR BINARY RESPONSES

Introduction
Single-level logit and probit regression models for dichotomous responses

Generalized linear model formulation
Latent-response formulation

Logistic regression
Probit regression

Which treatment is best for toenail infection?
Longitudinal data structure
Proportions and fitted population-averaged or marginal probabilities
Random-intercept logistic regression

Model specification

Reduced-form specification
Two-stage formulation

Estimation of random-intercept logistic models

Using xtlogit
Using xtmelogit
Using gllamm

Subject-specific or conditional vs. population-averaged or marginal relationships
Measures of dependence and heterogeneity

Conditional or residual intraclass correlation of the latent responses
Median odds ratio
Measures of association for observed responses at median fixed part of the model

Inference for random-intercept logistic models

Tests and confidence intervals for odds ratios
Tests of variance components

Maximum likelihood estimation

Adaptive quadrature
Some speed and accuracy considerations

Advice for speeding up estimation in gllamm

Assigning values to random effects

Maximum “likelihood” estimation
Empirical Bayes prediction
Empirical Bayes modal prediction

Different kinds of predicted probabilities

Predicted population-averaged or marginal probabilities
Predicted subject-specific probabilities

Predictions for hypothetical subjects: Conditional probabilities
Predictions for the subjects in the sample: Posterior mean probabilities

Other approaches to clustered dichotomous data

Conditional logistic regression
Generalized estimating equations (GEE)

Summary and further reading
Exercises

 

11. ORDINAL RESPONSES

Introduction
Single-level cumulative models for ordinal responses

Generalized linear model formulation
Latent-response formulation
Proportional odds
Identification

Are antipsychotic drugs effective for patients with schizophrenia?
Longitudinal data structure and graphs

Longitudinal data structure
Plotting cumulative proportions
Plotting cumulative sample logits and transforming the time scale

A single-level proportional odds model

Model specification
Estimation using Stata

A random-intercept proportional odds model

Model specification
Estimation using Stata
Measures of dependence and heterogeneity

Residual intraclass correlation of latent responses
Median odds ratio

A random-coefficient proportional odds model

Model specification
Estimation using gllamm

Different kinds of predicted probabilities

Predicted population-averaged or marginal probabilities
Predicted subject-specific probabilities: Posterior mean

Do experts differ in their grading of student essays?
A random-intercept probit model with grader bias

Model specification
Estimation using gllamm

Including grader-specific measurement error variances

Model specification
Estimation using gllamm

Including grader-specific thresholds

Model specification
Estimation using gllamm

Other link functions

Cumulative complementary log-log model
Continuation-ratio logit model
Adjacent-category logit model
Baseline-category logit and stereotype models

Summary and further reading
Exercises

 

12. NOMINAL RESPONSES AND DISCRETE CHOICE

Introduction
Single-level models for nominal responses

Multinomial logit models
Conditional logit models

Classical conditional logit models
Conditional logit models also including covariates that vary only over units

Independence from irrelevant alternatives
Utility-maximization formulation
Does marketing affect choice of yogurt?
Single-level conditional logit models

Conditional logit models with alternative-specific intercepts

Multilevel conditional logit models

Preference heterogeneity: Brand-specific random intercepts
Response heterogeneity: Marketing variables with random coefficients
Preference and response heterogeneity

Estimation using gllamm
Estimation using mixlogit

Prediction of random effects and response probabilities
Summary and further reading
Exercises

 

VI Models for counts

 

13. COUNTS

Introduction
What are counts?

Counts versus proportions
Counts as aggregated event-history data

Single-level Poisson models for counts
Did the German health-care reform reduce the number of doctor visits?
Longitudinal data structure
Single-level Poisson regression

Model specification
Estimation using Stata

Random-intercept Poisson regression

Model specification
Measures of dependence and heterogeneity
Estimation using Stata

Using xtpoisson
Using xtmepoisson
Using gllamm

Random-coefficient Poisson regression

Model specification
Estimation using Stata

Using xtmepoisson
Using gllamm

Interpretation of estimates

Overdispersion in single-level models

Normally distributed random intercept

Negative binomial models

Mean dispersion or NB2
Constant dispersion or NB1

Quasilikelihood

Level-1 overdispersion in two-level models
Other approaches to two-level count data

Conditional Poisson regression
Conditional negative binomial regression
Generalized estimating equations

Marginal and conditional effects when responses are MAR
Which Scottish counties have a high risk of lip cancer?
Standardized mortality ratios
Random-intercept Poisson regression

Model specification
Estimation using gllamm
Prediction of standardized mortality ratios

Nonparametric maximum likelihood estimation

Specification
Estimation using gllamm
Prediction

Summary and further reading
Exercises

 

VII Models for survival or duration data

 

Introduction to models for survival or duration data (part VII)

 

14. DISCRETE-TIME SURVIVAL

Introduction
Single-level models for discrete-time survival data

Discrete-time hazard and discrete-time survival
Data expansion for discrete-time survival analysis
Estimation via regression models for dichotomous responses
Including covariates

Time-constant covariates
Time-varying covariates

Multiple absorbing events and competing risks
Handling left-truncated data

How does birth history affect child mortality?
Data expansion
Proportional hazards and interval-censoring
Complementary log-log models
A random-intercept complementary log-log model

Model specification
Estimation using Stata

Population-averaged or marginal vs. subject-specific or conditional survival probabilities
Summary and further reading
Exercises

 

15. CONTINUOUS-TIME SURVIVAL

Introduction
What makes marriages fail?
Hazards and survival
Proportional hazards models

Piecewise exponential model
Cox regression model
Poisson regression with smooth baseline hazard

Accelerated failure-time models

Log-normal model

Time-varying covariates
Does nitrate reduce the risk of angina pectoris?
Marginal modeling

Cox regression
Poisson regression with smooth baseline hazard

Multilevel proportional hazards models

Cox regression with gamma shared frailty
Poisson regression with normal random intercepts
Poisson regression with normal random intercept and random coefficient

Multilevel accelerated failure-time models

Log-normal model with gamma shared frailty
Log-normal model with log-normal shared frailty

A fixed-effects approach

Cox regression with subject-specific baseline hazards

Different approaches to recurrent-event data

Total time
Counting process
Gap time

Summary and further reading
Exercises

 

VIII Models with nested and crossed random effects

 

16. MODELS WITH NESTED AND CROSSED RANDOM EFFECTS

Introduction
Did the Guatemalan immunization campaign work?
A three-level random-intercept logistic regression model

Model specification
Measures of dependence and heterogeneity

Types of residual intraclass correlations of the latent responses
Types of median odds ratios

Three-stage formulation

Estimation of three-level random-intercept logistic regression models

Using gllamm
Using xtmelogit

A three-level random-coefficient logistic regression model
Estimation of three-level random-coefficient logistic regression models

Using gllamm
Using xtmelogit

Prediction of random effects

Empirical Bayes prediction
Empirical Bayes modal prediction

Different kinds of predicted probabilities

Predicted population-averaged or marginal probabilities: New clusters
Predicted median or conditional probabilities
Predicted posterior mean probabilities: Existing clusters

Do salamanders from different populations mate successfully?
Crossed random-effects logistic regression
Summary and further reading
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: Sophia Rabe-Hesketh and Anders Skrondal
Edition: Third Edition
ISBN-13: 978-1-59718-104-4
©Copyright: 2012
Versione e-Book disponibile

Volume II is devoted to generalized linear mixed models for binary, categorical, count, and survival outcomes. The second volume has seven chapters also organized into four parts. The first three parts in volume II cover models for categorical responses, including binary, ordinal, and nominal (a new chapter); models for count data; and models for survival data, including discrete-time and continuous-time (a new chapter) survival responses. The fourth and final part in volume II describes models with nested and crossed-random effects with an emphasis on binary outcomes.