Regression Models for Categorical Dependent Variables Using Stata, Third Edition

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Regression Models for Categorical Dependent Variables Using Stata, Third Edition, by J. Scott Long and Jeremy Freese, is an essential reference for those who use Stata to fit and interpret regression models for categorical data. Although regression models for categorical dependent variables are common, few texts explain how to interpret such models; this text decisively fills the void.

 

The third edition is divided into two parts. Part I begins with an excellent introduction to Stata and follows with general treatments of the estimation, testing, fitting, and interpretation of models for categorical dependent variables. The book is thus accessible to new users of Stata and those who are new to categorical data analysis. Part II is devoted to a comprehensive treatment of estimation and interpretation for binary, ordinal, nominal, and count outcomes.

 

Readers familiar with previous editions will find many changes in the third edition. An entire chapter is now devoted to interpretation of regression models using predictions. This concept is explored in greater depth in Part II. The authors also discuss how many improvements made to Stata in recent years—factor variables, marginal effects with margins, plotting predictions using marginsplot—facilitate analysis of categorical data.

 

The authors advocate a variety of new methods that use predictions to interpret the effect of variables in regression models. Readers will find all discussion of statistical concepts firmly grounded in concrete examples. All the examples, datasets, and author-written commands are available on the authors' website, so readers can easily replicate the examples with Stata.

 

Examples in the new edition also illustrate changes to the authors' popular SPost commands after a recent rewrite inspired by the authors' evolving views on interpretation. Readers will note that SPost now takes full advantage of the power of the margins command and the flexibility of factor-variable notation. Long and Freese also provide a suite of new commands, including mchangemtable, and mgen. These commands complement margins, aiding model interpretation, hypothesis testing, and model diagnostics. They offer the same syntactical convenience features that users of Stata expect, for example including powers or interactions of covariates in regression models and seamlessly working with complex survey data. The authors also discuss how to use these commands to estimate marginal effects, either averaged over the sample or evaluated at fixed values of the regressors.

 

The third edition of Regression Models for Categorical Dependent Variables Using Stata continues to provide the same high-quality, practical tutorials of previous editions. It also offers significant improvements over previous editions—new content, updated information about Stata, and updates to the authors' own commands. This book should be on the bookshelf of every applied researcher analyzing categorical data and is an invaluable learning resource for students and others who are new to categorical data analysis.

 

Scott Long is Distinguished Professor of Sociology and Statistics at Indiana University–Bloomington. He has contributed articles to many journals, including the American Sociological Review, American Journal of Sociology, American Statistician, and Sociological Methods and Research. Dr. Long has authored or edited seven previous books on statistics, including the highly acclaimed Regression Models for Categorical and Limited Dependent Variables and The Workflow of Data Analysis Using Stata. In 2001, he received the Paul Lazarsfeld Memorial Award for Distinguished Contributions to Sociological Methodology. He is an elected Fellow of the American Statistical Association and a member of the Sociological Research Association.

 

Jeremy Freese is Ethel and John Lindgren Professor of Sociology and Faculty Fellow of the Institute for Policy Research at Northwestern University. He has previously been a faculty member at the University of Wisconsin–Madison and a Robert Wood Johnson Scholar in Health Policy Research at Harvard University. He has published numerous research articles in journals, including the American Sociological Review, American Journal of Sociology, and Public Opinion Quarterly. He has also taught categorical data analysis at the ICPSR Summer Program in Quantitative Methods and at El Colegio de México.

 

 

List of figures
Preface (PDF)
Part I   General information
1 Introduction
1.1 What is this book about? 
1.2 Which models are considered? 
1.3 Whom is this book for? 
1.4 How is the book organized? 
1.5 The SPost software
1.5.1 Updating Stata
1.5.2 Installing SPost13
Uninstalling SPost9 
Installing SPost13 using search 
Installing SPost13 using net install
1.5.3 Uninstalling SPost13
1.6 Sample do-files and datasets
1.6.1 Installing the spost13_do package 
1.6.2 Using spex to load data and run examples
1.7 Getting help with SPost
1.7.1 What if an SPost command does not work? 
1.7.2 Getting help from the authors
What we need to help you
1.8 Where can I learn more about the models?
2 Introduction to Stata
2.1 The Stata interface 
2.2 Abbreviations 
2.3 Getting help
2.3.1 Online help 
2.3.2 PDF manuals 
2.3.3 Error messages 
2.3.4 Asking for help 
2.3.5 Other resources
2.4 The working directory 
2.5 Stata file types 
2.6 Saving output to log files 
2.7 Using and saving datasets
2.7.1 Data in Stata format 
2.7.2 Data in other formats 
2.7.3 Entering data by hand
2.8 Size limitations on datasets 
2.9 Do-files
2.9.1 Adding comments 
2.9.2 Long lines 
2.9.3 Stopping a do-file while it is running 
2.9.4 Creating do-files 
2.9.5 Recommended structure for do-files
2.10 Using Stata for serious data analysis 
2.11 Syntax of Stata commands
2.11.1 Commands 
2.11.2 Variable lists 
2.11.3 if and in qualifiers 
2.11.4 Options
2.12 Managing data
2.12.1 Looking at your data 
2.12.2 Getting information about variables 
2.12.3 Missing values 
2.12.4 Selecting observations 
2.12.5 Selecting variables
2.13 Creating new variables
2.13.1 The generate command 
2.13.2 The replace command 
2.13.3 The recode command
2.14 Labeling variables and values
2.14.1 Variable labels 
2.14.2 Value labels 
2.14.3 The notes command
2.15 Global and local macros 
2.16 Loops using foreach and forvalues 
2.17 Graphics
2.17.1 The graph command
2.18 A brief tutorial 
2.19 A do-file template 
2.20 Conclusion
3 Estimation, testing, and fit
3.1 Estimation
3.1.1 Stata’s output for ML estimation 
3.1.2 ML and sample size 
3.1.3 Problems in obtaining ML estimates 
3.1.4 Syntax of estimation commands 
3.1.5 Variable lists 
Using factor-variable notation in the variable list 
Specifying interaction and polynomials 
More on factor-variable notation
3.1.6 Specifying the estimation sample
Missing data 
Information about missing values 
Postestimation commands and the estimation sample
3.1.7 Weights and survey data
Complex survey designs
3.1.8 Options for regression models 
3.1.9 Robust standard errors 
3.1.10 Reading the estimation output 
3.1.11 Storing estimation results 
(Advanced) Saving estimates to a file
3.1.12 Reformatting output with estimates table 
3.2 Testing
3.2.1 One-tailed and two-tailed tests 
3.2.2 Wald and likelihood-ratio tests 
3.2.3 Wald tests with test and testparm 
3.2.4 LR tests with lrtest
Avoiding invalid LR tests
3.3 Measures of fit
3.3.1 Syntax of fitstat 
3.3.2 Methods and formulas used by fitstat 
3.3.3 Example of fitstat 
3.4 estat postestimation commands 
3.5 Conclusion
4 Methods of interpretation
4.1 Comparing linear and nonlinear models 
4.2 Approaches to interpretation
4.2.1 Method of interpretation based on predictions
4.2.2 Method of interpretation using parameters 
4.2.3 Stata and SPost commands for interpretation
4.3 Predictions for each observation 
4.4 Predictions at specified values
4.4.1 Why use the m* commands instead of margins? 
4.4.2 Using margins for predictions
Predictions using interaction and polynomial terms 
Making multiple predictions 
Predictions for groups defined by levels of categorical variables 
4.4.3 (Advanced) Nondefault predictions using margins
The predict() option 
The expression() option 
4.4.4 Tables of predictions using mtable
mtable with categorical and count outcomes 
(Advanced) Combining and formatting tables using mtable
4.5 Marginal effects: Changes in predictions
4.5.1 Marginal effects using margins 
4.5.2 Marginal effects using mtable 
4.5.3 Posting predictions and using mlincom 
4.5.4 Marginal effects using mchange
4.6 Plotting predictions
4.6.1 Plotting predictions with marginsplot 
4.6.2 Plotting predictions using mgen
4.7 Interpretation of parameters
4.7.1 The listcoef command 
4.7.2 Standardized coefficients 
4.7.3 Factor and percentage change coefficients
4.8 Next steps
Part II   Models for specific kinds of outcomes
5 Models for binary outcomes: Estimation, testing, and fit
5.1 The statistical model
5.1.1 A latent-variable model 
5.1.2 A nonlinear probability model
5.2 Estimation using logit and probit commands
5.2.1 Example of logit model 
5.2.2 Comparing logit and probit 
5.2.3 (Advanced) Observations predicted perfectly
5.3 Hypothesis testing
5.3.1 Testing individual coefficients 
5.3.2 Testing multiple coefficients 
5.3.3 Comparing LR and Wald tests
5.4 Predicted probabilities, residuals, and influential observations
5.4.1 Predicted probabilities using predict 
5.4.2 Residuals and influential observations using predict 
5.4.3 Least likely observations
5.5 Measures of fit
5.5.1 Information criteria 
5.5.2 Pseudo-R²'s 
5.5.3 (Advanced) Hosmer–Lemeshow statistic
5.6 Other commands for binary outcomes 
5.7 Conclusion
6 Models for binary outcomes: Interpretation
6.1 Interpretation using regression coefficients
6.1.1 Interpretation using odds ratios 
6.1.2 (Advanced) Interpretation using y*
6.2 Marginal effects: Changes in probabilities
6.2.1 Linked variables 
6.2.2 Summary measures of change
MEMs and MERs 
AMEs 
Standard errors of marginal effects
6.2.3 Should you use the AME, the MEM, or the MER? 
6.2.4 Examples of marginal effects
AMEs for continuous variables 
AMEs for factor variables 
Summary table of AMEs 
Marginal effects for subgroups 
MEMs and MERs 
Marginal effects with powers and interactions
6.2.5 The distribution of marginal effects 
6.2.6 (Advanced) Algorithm for computing the distribution of effects
6.3 Ideal types
6.3.1 Using local means with ideal types 
6.3.2 Comparing ideal types with statistical tests 
6.3.3 (Advanced) Using macros to test differences between ideal types 
6.3.4 Marginal effects for ideal types
6.4 Tables of predicted probabilities 
6.5 Second differences comparing marginal effects 
6.6. Graphing predicted probabilities
6.6.1 Using marginsplot 
6.6.2 Using mgen with the graph command 
6.6.3 Graphing multiple predictions 
6.6.4 Overlapping confidence intervals 
6.6.5 Adding power terms and plotting predictions 
6.6.6 (Advanced) Graphs with local means
6.7 Conclusion
7 Models for ordinal outcomes
7.1 The statistical model
7.1.1 A latent-variable model 
7.1.2 A nonlinear probability model
7.2 Estimation using ologit and oprobit
7.2.1 Example of ordinal logit mdel 
7.2.2 Predicting perfectly
7.3 Hypothesis testing
7.3.1 Testing individual coefficients 
7.3.2 Testing multiple coefficients
7.4 Measures of fit using fitstat 
7.5 (Advanced) Converting to a different parameterization 
7.6 The parallel regression assumption
7.6.1 Testing the parallel regression assumption using oparallel 
7.6.2 Testing the parallel regression assumption using brant 
7.6.3 Caveat regarding the parallel regression assumption 
7.7 Overview of interpretation 
7.8 Interpreting transformed coefficients
7.8.1 Marginal change in y* 
7.8.2 Odds ratios
7.9 Interpretations based on predicted probabilities 
7.10 Predicted probabilities with predict 
7.11 Marginal effects
7.11.1 Plotting marginal effects 
7.11.2 Marginal effects for a quick overview
7.12 Predicted probabilities for ideal types
7.12.1 (Advanced) Testing differences between ideal types
7.13 Tables of predicted probabilities 
7.14 Plotting predicted probabilities 
7.15 Probability plots and marginal effects 
7.16 Less common models for ordinal outcomes
7.16.1 The stereotype logistical model 
7.16.2 The generalized ordered logit model 
7.16.3 (Advanced) Predictions without using factor-variable notation 
7.16.4 The sequential logit model
7.17 Conclusion
8 Models for nominal outcomes
8.1 The multinomial logit model
8.1.1 Formal statement of the model
8.2 Estimation using the mlogit command
Weights and complex samples 
Options
8.2.1 Examples of MNLM 
8.2.2 Selecting different base outcomes 
8.2.3 Predicting perfectly
8.3 Hypothesis testing
8.3.1 mlogtest for tests of the MNLM 
8.3.2 Testing the effects of the independent variables 
8.3.3 Tests for combining alternatives
8.4 Independence of irrelevant alternatives
8.4.1 Hausman-McFadden test of IIA 
8.4.2 Small-Hsiao test of IIA
8.5 Measures of fit 
8.6 Overview of interpretation 
8.7 Predicted probabilities with predict 
8.8 Marginal effects
8.8.1 (Advanced) The distribution of marginal effects
8.9 Tables of predicted probabilities
8.9.1 (Advanced) Testing second differences 
8.9.2 (Advanced) Predictions using local means and subsamples
8.10 Graphing predicted probabilities 
8.11 Odds ratios
8.11.1 Listing odds ratios with listcoef 
8.11.2 Plotting odds ratios
8.12 (Advanced) Additional models for nominal outcomes
8.12.1 Stereotype logistic regression 
8.12.2 Conditional logit model 
8.12.3 Multinomial probit model with IIA 
8.12.4 Alternative-specific multinomial probit 
8.12.5 Rank-ordered logit model
8.13 Conclusion
9 Models for count outcomes
9.1 The Poisson distribution
9.1.1 Fitting the Poisson distribution with the poisson command 
9.1.2 Compaing observed and predicted counts with mgen
9.2 The Poisson regression model
9.2.1 Estimation using poisson
Example of the PRM
9.2.2 Factor and percentage changes in E(y | x)
Example of factor and percentage change
9.2.3 Marginal effects on E(y | x)
Examples of marginal effects
9.2.4 Interpretation using predicted probabilities
Predicted probabilities using mtable and mchange 
Treating a count independent variable as a factor variable 
Predicted probabilities using mgen
9.2.5 Comparing observed and predicted counts to evaluate model specification 
9.2.6 (Advanced) Exposure time
9.3 The negative binomial regression model
9.3.1 Estimation using nbreg
NB1 and NB2 variance functions
9.3.2 Example of NBRM 
9.3.3 Testing for overdispersion 
9.3.4 Comparing the PRM and NBRM using estimates table 
9.3.5 Robust standard errors 
9.3.6 Interpretation using E(y | x) 
9.3.7 Interpretation using predicted probabilities
9.4 Models for truncated counts
9.4.1 Estimation using tpoisson and tnbreg
Example of zero-truncated model
9.4.2 Interpretation using E(y | x) 
9.4.3 Predictions in the estimation sample 
9.4.4 Interpretation using predicted rates and probabilities
9.5 (Advanced) The hurdle regression model
9.5.1 Fitting the hurdle model 
9.5.2 Predictions in the sample 
9.5.3 Predictions at user-specified values 
9.5.4 Warning regarding sample specification
9.6 Zero-inflated count models
9.6.1 Estimation using zinb and zip 
9.6.2 Example of zero-inflated models 
9.6.3 Interpretation of coefficients 
9.6.4 Interpretation of predicted probabilities
Predicted probabilities with mtable 
Plotting predicted probabilities with mgen
9.7 Comparisons among count models
9.7.1 Comparing mean probabilities 
9.7.2 Tests to compare count models 
9.7.3 Using countfit to compare count models
9.8 Conclusion
References 
Author index (PDF) 
Subject index (PDF)