Multilevel and Longitudinal Modeling Using Stata Volume I: Continuous Responses

Volume I is devoted to continuous Gaussian linear mixed models and has nine chapters organized into four parts. The first part reviews the methods of linear regression. The second part provides in-depth coverage of two-level models, the simplest extensions of a linear regression model.

 

Rabe-Hesketh and Skrondal begin with the comparatively simple random-intercept linear model without covariates, developing the mixed 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 mixed-model 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 then discuss models with random coefficients.

 

The third part of volume I describes models for longitudinal and panel data, including dynamic models, marginal models (a new chapter), and growth-curve models (a new chapter). The fourth and final part covers models with nested and crossed random effects, including a new chapter describing in more detail higher-level nested models for continuous outcomes.

 

The mixed-model foundation and the in-depth coverage of the mixed-model principles provided in volume I for continuous outcomes make it straightforward to transition to generalized linear mixed models for noncontinuous outcomes, which are described in volume II.

List of Tables
List of Figures
Preface
Multilevel and longitudinal models: When and why?

 

I Preliminaries

 

1. REVIEW OF LINEAR REGRESSION

Introduction
Is there gender discrimination in faculty salaries?
Independent-samples t test
One-way analysis of variance
Simple linear regression
Dummy variables
Multiple linear regression
Interactions
Dummy variables for more than two groups
Other types of interactions

Interaction between dummy variables
Interaction between continuous covariates

Nonlinear effects
Residual diagnostics
Causal and noncausal interpretations of regression coefficients

Regression as conditional expectation
Regression as structural model

Summary and further reading
Exercises

 

II Two-level models

 

2. VARIANCE-COMPONENTS MODELS

Introduction
How reliable are peak-expiratory-flow measurements?
Inspecting within-subject dependence
The variance-components model

Model specification
Path diagram
Between-subject heterogeneity
Within-subject dependence

Intraclass correlation
Intraclass correlation versus Pearson correlation

Estimation using Stata

Data preparation: Reshaping to long form
Using xtreg
Using xtmixed

Hypothesis tests and confidence intervals

Hypothesis test and confidence interval for the population mean
Hypothesis test and confidence interval for the between-cluster variance

Likelihood-ratio test
F test
Confidence intervals

Model as data-generating mechanism
Fixed versus random effects
Crossed versus nested effects
Parameter estimation

Model assumptions

Mean structure and covariance structure
Distributional assumptions

Different estimation methods
Inference for β

Estimate and standard error: Balanced case
Estimate: Unbalanced case

Assigning values to the random intercepts

Maximum “likelihood” estimation

Implementation via OLS regression
Implementation via the mean total residual

Empirical Bayes prediction
Empirical Bayes standard errors

Comparative standard errors
Diagnostic standard errors

Summary and further reading
Exercises

 

3. RANDOM-INTERCEPT MODELS WITH COVARIATES

Introduction
Does smoking during pregnancy affect birthweight?

Data structure and descriptive statistics

The linear random-intercept model with covariates

Model specification
Model assumptions
Mean structure
Residual variance and intraclass correlation
Graphical illustration of random-intercept model

Estimation using Stata

Using xtreg
Using xtmixed

Coefficients of determination or variance explained
Hypothesis tests and confidence intervals

Hypothesis tests for regression coefficients

Hypothesis tests for individual regression coefficients
Joint hypothesis tests for several regression coefficients

Predicted means and confidence intervals
Hypothesis test for random-intercept variance

Between and within effects of level-1 covariates

Between-mother effects
Within-mother effects
Relations among estimators
Level-2 endogeneity and cluster-level confounding
Allowing for different within and between effects
Hausman endogeneity test

Fixed versus random effects revisited
Assigning values to random effects: Residual diagnostics
More on statistical inference

Overview of estimation methods
Consequences of using standard regression modeling for clustered data
Power and sample-size determination

Summary and further reading
Exercises

 

4. RANDOM-COEFFICIENT MODELS

Introduction
How effective are different schools?
Separate linear regressions for each school
Specification and interpretation of a random-coefficient model

Specification of a random-coefficient model
Interpretation of the random-effects variances and covariances

Estimation using xtmixed

Random-intercept model
Random-coefficient model

Testing the slope variance
Interpretation of estimates
Assigning values to the random intercepts and slopes

Maximum “likelihood” estimation
Empirical Bayes prediction
Model visualization
Residual diagnostics
Inferences for individual schools

Two-stage model formulation
Some warnings about random-coefficient models

Meaningful specification
Many random coefficients
Convergence problems
Lack of identification

Summary and further reading
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

Introduction
Conventional random-intercept model
Random-intercept models accommodating endogenous covariates

Consistent estimation of effects of endogenous time-varying covariates
Consistent estimation of effects of endogenous time-varying and endogenous time-constant covariates

Fixed-intercept model

Using xtreg or regress with a differencing operator
Using anova

Random-coefficient model
Fixed-coefficient model
Lagged-response or dynamic models

Conventional lagged-response model
Lagged-response model with subject-specific intercepts

Missing data and dropout

Maximum likelihood estimation under MAR: A simulation

Summary and further reading
Exercises

 

6. MARGINAL MODELS

Introduction
Mean structure
Covariance structures

Unstructured covariance matrix
Random-intercept or compound symmetric/exchangeable structure
Random-coefficient structure
Autoregressive and exponential structures
Moving-average residual structure
Banded and Toeplitz structures

Hybrid and complex marginal models

Random effects and correlated level-1 residuals
Heteroskedastic level-1 residuals over occasions
Heteroskedastic level-1 residuals over groups
Different covariance matrices over groups

Comparing the fit of marginal models
Generalized estimating equations (GEE)
Marginal modeling with few units and many occasions

Is a highly organized labor market beneficial for economic growth?
Marginal modeling for long panels
Fitting marginal models for long panels in Stata

Summary and further reading
Exercises

 

7. GROWTH-CURVE MODELS

Introduction
How do children grow?

Observed growth trajectories

Models for nonlinear growth

Polynomial models

Fitting the models
Predicting the mean trajectory
Predicting trajectories for individual children

Piecewise linear models

Fitting the models
Predicting the mean trajectory

Two-stage model formulation
Heteroskedasticity

Heteroskedasticity at level 1
Heteroskedasticity at level 2

How does reading improve from kindergarten through third grade?
Growth-curve model as a structural equation model

Estimation using sem
Estimation using xtmixed

Summary and further reading
Exercises

 

IV Models with nested and crossed random effects

 

8. HIGHER-LEVEL MODELS WITH NESTED RANDOM EFFECTS

Introduction
Do peak-expiratory-flow measurements vary between methods within subjects?
Inspecting sources of variability
Three-level variance-components models
Different types of intraclass correlation
Estimation using xtmixed
Empirical Bayes prediction
Testing variance components
Crossed versus nested random effects revisited
Does nutrition affect cognitive development of Kenyan children?
Describing and plotting three-level data

Data structure and missing data
Level-1 variables
Level-2 variables
Level-3 variables
Plotting growth trajectories

Three-level random-intercept model

Model specification: Reduced form
Model specification: Three-stage formulation
Estimation using xtmixed

Three-level random-coefficient models

Random coefficient at the child level
Random coefficient at the child and school levels

Residual diagnostics and predictions
Summary and further reading
Exercises

 

9. CROSSED RANDOM EFFECTS

Introduction
How does investment depend on expected profit and capital stock?
A two-way error-components model

Model specification
Residual variances, covariances, and intraclass correlations

Longitudinal correlations
Cross-sectional correlations

Estimation using xtmixed
Prediction

How much do primary and secondary schools affect attainment at age 16?
Data structure
Additive crossed random-effects model

Specification
Estimation using xtmixed

Crossed random-effects model with random interaction

Model specification
Intraclass correlations
Estimation using xtmixed
Testing variance components
Some diagnostics

A trick requiring fewer random effects
Summary and further reading
Exercises

 

A. USEFUL STATA COMMANDS

 

References

Author: Sophia Rabe-Hesketh and Anders Skrondal
Edition: Third Edition
ISBN-13: 978-1-59718-103-7
©Copyright: 2012
Versione e-Book disponibile

Volume I is devoted to continuous Gaussian linear mixed models and has nine chapters organized into four parts. The first part reviews the methods of linear regression. The second part provides in-depth coverage of two-level models, the simplest extensions of a linear regression model.