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E-raamat: Regression Models for Categorical and Count Data

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Regression Models for Categorical and Count DataSuurem pilt
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In this engaging and well-illustrated volume of the SAGE Quantitative Research Kit, Peter Martin provides practical guidance on conducting regression analysis on categorical and count data. The author covers both the theory and application of statistical models, with the help of illuminating graphs.


This text provides practical guidance on conducting regression analysis on categorical and count data. Step by step and supported by lots of helpful graphs, it covers both the theoretical underpinnings of these methods as well as their application, giving you the skills needed to apply them to your own research. It offers guidance on:

  • Using logistic regression models for binary, ordinal, and multinomial outcomes
  • Applying count regression, including Poisson, negative binomial, and zero-inflated models
  • Choosing the most appropriate model to use for your research
  • The general principles of good statistical modelling in practice.

Part of The SAGE Quantitative Research Kit, this book will give you the know-how and confidence needed to succeed on your quantitative research journey

Arvustused

An accessible but rigorous introduction to data analysis that makes good use of real-world examples. The focus in this book on categorical and count data makes it particularly appropriate for social scientists who are often aiming to understand the predictors of social phenomena that cannot be measured numerically. -- Jane Elliott Anyone willing to learn about regression for the first time, as well as readers already familiar with the topic, can dive straight into this book and will be positively surprised by its clarity and accessibility. It covers everything one has to know when it comes to regression models for categorical and count data. [ ...] It has very apt examples and a clear style of writing. I think that the author has done a great job of keeping all the explanations as understandable as possible, making them accessible to anyone interested in the topic. All in all, this is an extremely good book and I highly recommend it if you want to learn more about regression. -- Antonella Cirasola This book succeeds in giving a great outline of a large number of different statistical modelling techniques, with a streamlined narrative that makes essential links between them. Instead of completely separate chapters, the books format builds upon the information of different sections to provide the reader with concise yet thorough knowledge of some of the most relevant techniques used in data-driven research. The simple and comprehensive way in which Peter guides us to interpret the variety of estimated coefficients of the different regression models explored is superb. Moreover, the last chapter provides essential directions on decision-making in the process of research when selecting and implementing some of the statistical modelling techniques covered in the book. This section is a call to us researchers to critically examined our research problems and make reasoned decisions about them instead of just following a statistical recipe. -- Eliazar Luna

List of Figures, Tables and Boxes
ix
About the Author xv
Acknowledgements xvii
Preface xix
1 Introduction
1(14)
Why Study Regression Models for Categorical and Count Data?
2(1)
A Few Words on Terminology
3(1)
Outcome and Predictor
3(1)
Types of Variables
3(1)
Why Do We Need to Look Beyond Linear Regression?
4(1)
Regression Beyond the Linear Model: An Illustrated Introduction
4(4)
Linear Regression: A Reminder, With Some Mathematical Notation
8(1)
Regression Model and Notation
8(1)
Errors and Residuals
9(1)
Estimation and Partition of Outcome Variance
9(1)
Generalised Linear Models
10(1)
What's the Same and What's Different
11(2)
How You Might Use This Book
13(2)
2 Logistic Regression
15(64)
What Is Logistic Regression?
16(1)
Probabilities and Conditional Probabilities
17(1)
Simple Example of Data With a Binary Outcome
18(2)
Analysis of a 2 × 2 Table: Probabilities, Odds and Odds Ratios
20(1)
Probabilities
20(1)
Risk Ratio and Absolute Risk Difference
20(1)
Odds
21(2)
Log Odds: The Logit Transformation
23(2)
Odds Ratio
25(1)
Logistic Regression: The Model
26(2)
Logistic Regression With a Single Categorical Predictor
28(1)
Predicted Probabilities
29(1)
Estimated Odds Ratio From a Logistic Regression Model
30(1)
Don't the Numbers Look Familiar?
31(1)
Logistic Regression With Two Categorical Predictors
32(1)
A Simple Model With Two Categorical Predictors
32(1)
Modelling an Interaction
33(1)
Illustrating the Models With and Without an Interaction
34(1)
Odds Ratios
35(1)
Predicted Probabilities
36(1)
Logistic Regression With a Numeric Predictor
37(6)
Logistic Regression: Assumptions and Estimation
43(1)
The Binomial Distribution
43(2)
The Logistic Curve
45(2)
Maximum Likelihood Estimation: How the Coefficients Are Found
47(1)
Confidence Intervals
48(2)
Model Comparison and Hypothesis Tests
50(1)
Likelihood Ratio Test
50(2)
Wald Test (or z-Test)
52(1)
Logistic Regression: An Example With Multiple Predictors
53(4)
Model Evaluation
57(1)
Residuals in Logistic Regression
57(1)
Model Calibration: Graphical Exploration
58(2)
The Hosmer-Lemeshow Test of Model Calibration
60(3)
Model Quality Indices for Logistic Regression
63(2)
Interpretation of Effect Sizes and Graphical Illustration
65(2)
Things That Might Go Wrong: Estimation Problems
67(3)
Logistic Regression in Action
70(1)
Exploring the Relationship Between Age and Attending Pop Concerts
71(2)
Logistic Regression of Pop Concert Attendance on Six Predictors
73(2)
Non-Binary Categorical Variables
75(4)
3 Ordinal Logistic Regression: The Generalised Ordered Logit Model
79(32)
Modelling Ordinal Outcomes: Proportional Odds or Non-Proportional Odds?
80(7)
Calculating Predicted Probabilities
87(1)
The Proportional Odds Ordinal Logistic Regression Model
88(6)
Testing the Proportional Odds Assumption: Brant's Test
94(2)
Generalised Ordinal Logit Models: Full, Partial and Non-Proportional Odds
96(1)
A Case Where the Proportional Odds Assumption Is Not Met
96(2)
The Non-Proportional Odds Model
98(1)
The Partial Proportional Odds Model
99(2)
Likelihood Ratio Test Comparing Proportional Odds, Partial Proportional Odds and Non-Proportional Odds Models
101(1)
Ordinal Logistic Regression in Action
102(9)
4 Multinomial Logistic Regression
111(34)
Example Data for Multinomial Logistic Regression
112(2)
Relative Risks
114(2)
Relative Risk Ratios
116(1)
A Simple Example of Multinomial Logistic Regression
117(2)
The Multinomial Logistic Regression Model
119(2)
Predicted Probabilities
121(1)
Interpreting and Illustrating the Results From a Multinomial Logistic Model
122(1)
Example Research Question
122(1)
Interpreting Results From a Multinomial Logistic Model
123(1)
Illustrating Results From a Multinomial Logistic Model
124(1)
Hypothesis Tests and Confidence Intervals
125(1)
Likelihood Ratio Test for Comparison of Nested Models
126(2)
The z-Test for an Individual Coefficient
128(2)
Confidence Intervals
130(1)
Test for Combining Outcome Categories
131(1)
Multinomial Regression: Some Additional Comments
132(1)
How to Choose the Reference Outcome Category
132(1)
Categorical Predictors With Dummy Variables
133(1)
Multinomial Logistic Regression in Action
134(11)
5 Regression Models for Count Data
145(52)
Distributions for Count Data
147(1)
The Poisson Distribution
147(4)
The Negative Binomial Distribution
151(2)
Poisson Regression
153(1)
Research Example: Police Operations Against Street Vendors in Latin American Capitals
154(1)
Poisson Regression of Police Operations in Bogota
155(2)
The Incidence Rate Ratio
157(1)
Visualising the Estimated Regression Line From a Poisson Model
158(1)
Negative Binomial Regression
159(5)
Zero-Truncation: When No Zeroes Are Observed
164(1)
Too Many Zeroes: Zero-Inflation and Hurdle Models
165(1)
Zero-Inflated Count Distributions
166(1)
Count Distributions With Hurdles
167(1)
Models for Outcomes With Excess Zeroes
168(8)
Model Comparison and Inference
176(1)
Investigating Overdispersion: Poisson or Negative Binomial Model?
177(3)
Information Criteria
180(4)
Inference for Individual Parameters and Nested Models Within the Same Model Type
184(2)
On Standard Errors in Count Models
186(1)
Model Evaluation
186(1)
Deviance Residuals for Poisson and Negative Binomial Regression
187(3)
Offsets: Accounting for Population Size, Time of Exposure, or Area
190(1)
What Is an Offset, and Why Might We Need One?
190(1)
Research Example: Socio-Economic Differences in the Uptake Rate of Free Eye Tests
191(6)
6 The Practice of Modelling
197(30)
Decision-Making in Statistical Modelling
198(1)
Match Between the Statistical Model and the Aims of the Research
199(2)
Most Rules Are Just Guidelines
201(1)
Usually You Can't Be Sure That You Have Found the `Best' Model
201(2)
The Importance of the Analysts' Judgement
203(2)
Some General Principles That Apply Most of the Time
205(1)
What If We're Not Sure About Model Assumptions: Sensitivity Analysis
206(1)
How to Test a Finding: Replication and Out-of-Sample Prediction
207(2)
Statistical Models and Uncertainty
209(1)
Two Ways of Getting It Wrong: Overfitting and Underfitting
210(4)
Is Science in a Statistical Crisis? On p-Values and Hypothesis Tests
214(1)
Critique of Current Practice Around Statistical Hypothesis Tests
215(1)
What Is a Statistical Hypothesis Test Again?
215(3)
Misuses and Misunderstandings of p-Values
218(4)
Exclusive Focus on Hypothesis Tests Distracts From Other Useful Purposes of Models
222(2)
Beyond This Book: Other Types of Models
224(3)
Glossary 227(10)
References 237(6)
Index 243
 Dr Peter Martin is Lecturer in Applied Statistics at University College London. He has taught statistics to students of sociology, psychology, epidemiology, and other disciplines since 2003. One of the joys of being a statistician is that it opens doors to research collaborations with many people in diverse fields. Dr Martin has been involved in investigations in life course research, survey methodology, and the analysis of racism. In recent years his research has focused on health inequalities, psychotherapy, and the evaluation of healthcare services. He has a particular interest in topics around mental health.
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