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Practical Guide to Logistic Regression

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Practical Guide to Logistic Regression covers the key points of the basic logistic regression model and illustrates how to use it properly to model a binary response variable. This powerful methodology can be used to analyze data from various fields, including medical and health outcomes research, business analytics and data science, ecology, fisheries, astronomy, transportation, insurance, economics, recreation, and sports. By harnessing the capabilities of the logistic model, analysts can better understand their data, make appropriate predictions and classifications, and determine the odds of one value of a predictor compared to another.

Drawing on his many years of teaching logistic regression, using logistic-based models in research, and writing about the subject, Professor Hilbe focuses on the most important features of the logistic model. Serving as a guide between the author and readers, the book explains how to construct a logistic model, interpret coefficients and odds ratios, predict probabilities and their standard errors based on the model, and evaluate the model as to its fit. Using a variety of real data examples, mostly from health outcomes, the author offers a basic step-by-step guide to developing and interpreting observation and grouped logistic models as well as penalized and exact logistic regression. He also gives a step-by-step guide to modeling Bayesian logistic regression.

R statistical software is used throughout the book to display the statistical models while SAS and Stata codes for all examples are included at the end of each chapter. The example code can be adapted to readers’ own analyses. All the code is available on the author’s website.

Author(s): Joseph M. Hilbe
Publisher: Chapman and Hall/CRC
Year: 2015

Language: English
Pages: 174

Cover
Title Page
Copyright Page
Table of Contents
Preface
Author
1 Statistical Models
1.1 What Is a Statistical Model?
1.2 Basics of Logistic Regression Modeling
1.3 The Bernoulli Distribution
1.4 Methods of Estimation
SAS Code
Stata Code
2 Logistic Models: Single Predictor
2.1 Models with a Binary Predictor
2.2 Predictions, Probabilities, and Odds Ratios
2.3 Basic Model Statistics
2.3.1 Standard Errors
2.3.2 z Statistics
2.3.3 p-Values
2.3.4 Confidence Intervals
2.4 Models with a Categorical Predictor
2.5 Models with a Continuous Predictor
2.5.1 Varieties of Continuous Predictors
2.5.2 A Simple GAM
2.5.3 Centering
2.5.4 Standardization
2.6 Prediction
2.6.1 Basics of Model Prediction
2.6.2 Prediction Confidence Intervals
SAS Code
Stata Code
3 Logistic Models: Multiple Predictors
3.1 Selection and Interpretation of Predictors
3.2 Statistics in a Logistic Model
3.3 Information Criterion Tests
3.3.1 Akaike Information Criterion
3.3.2 Finite Sample
3.3.3 Bayesian Information Criterion
3.3.4 Other Information Criterion Tests
3.4 The Model Fitting Process: Adjusting Standard Errors
3.4.1 Scaling Standard Errors
3.4.2 Robust or Sandwich Variance Estimators
3.4.3 Bootstrapping
3.5 Risk Factors, Confounders, Effect Modifiers, and Interactions
SAS Code
Stata Code
4 Testing and Fitting a Logistic Model
4.1 Checking Logistic Model Fit
4.1.1 Pearson Chi2 Goodness-of-Fit Test
4.1.2 Likelihood Ratio Test
4.1.3 Residual Analysis
4.1.4 Conditional Effects Plot
4.2 Classification Statistics
4.2.1 S–S Plot
4.2.2 ROC Analysis
4.2.3 Confusion Matrix
4.3 Hosmer–Lemeshow Statistic
4.4 Models with Unbalanced Data and Perfect Prediction
4.5 Exact Logistic Regression
4.6 Modeling Table Data
SAS Code
Stata Code
5 Grouped Logistic Regression
5.1 The Binomial Probability Distribution Function
5.2 From Observation to Grouped Data
5.3 Identifying and Adjusting for Extra Dispersion
5.4 Modeling and Interpretation of Grouped Logistic Regression
5.5 Beta-Binomial Regression
SAS Code
Stata Code
6 Bayesian Logistic Regression
6.1 A Brief Overview of Bayesian Methodology
6.2 Examples: Bayesian Logistic Regression
6.2.1 Bayesian Logistic Regression Using R
6.2.2 Bayesian Logistic Regression Using JAGS
6.2.3 Bayesian Logistic Regression with Informative Priors
SAS Code
Stata Code
Concluding Comments
References