Linear Regression Models
Applications in R
John P. Hoffmann
- 432 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Linear Regression Models
Applications in R
John P. Hoffmann
About This Book
Research in social and behavioral sciences has benefited from linear regression models (LRMs) for decades to identify and understand the associations among a set of explanatory variables and an outcome variable. Linear Regression Models: Applications in R provides you with a comprehensive treatment of these models and indispensable guidance about how to estimate them using the R software environment.
After furnishing some background material, the author explains how to estimate simple and multiple LRMs in R, including how to interpret their coefficients and understand their assumptions. Several chapters thoroughly describe these assumptions and explain how to determine whether they are satisfied and how to modify the regression model if they are not. The book also includes chapters on specifying the correct model, adjusting for measurement error, understanding the effects of influential observations, and using the model with multilevel data. The concluding chapter presents an alternative modelâlogistic regressionâdesigned for binary or two-category outcome variables. The book includes appendices that discuss data management and missing data and provides simulations in R to test model assumptions.
Features
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- Furnishes a thorough introduction and detailed information about the linear regression model, including how to understand and interpret its results, test assumptions, and adapt the model when assumptions are not satisfied.
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- Uses numerous graphs in R to illustrate the model's results, assumptions, and other features.
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- Does not assume a background in calculus or linear algebra, rather, an introductory statistics course and familiarity with elementary algebra are sufficient.
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- Provides many examples using real-world datasets relevant to various academic disciplines.
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- Fully integrates the R software environment in its numerous examples.
The book is aimed primarily at advanced undergraduate and graduate students in social, behavioral, health sciences, and related disciplines, taking a first course in linear regression. It could also be used for self-study and would make an excellent reference for any researcher in these fields. The R code and detailed examples provided throughout the book equip the reader with an excellent set of tools for conducting research on numerous social and behavioral phenomena.
John P. Hoffmann is a professor of sociology at Brigham Young University where he teaches research methods and applied statistics courses and conducts research on substance use and criminal behavior.
Frequently asked questions
Information
1 Introduction
Our Doubts are Traitors and Make Us Lose the Good We Oft Might Win2
- A single study is never the end of the story; multiple studies are needed before we can (or should) reach defensible conclusions about social and behavioral phenomena.
- Consumers and researchers need to embrace a healthy dose of skepticism when considering the results of research studies.5 They should ask questions about how data were collected, how variables were measured, and whether the appropriate statistical methods were used. We should also realize that random or sampling âerrorâ (see Chapter 2) affects the results of even the best designed studies.
- People should be encouraged to use their common sense and reasoning skills when assessing data and the results of analyses. Although itâs important to minimize confirmation bias and similar cognitive tendencies that (mis)shape how we process and interpret information, we should still consider whether research findings are based on sound premises and follow a logical pattern given what we already know about a phenomenon.
Best Statistical Practices6
- Plot your dataâearly and often.
- Understand that your dataset is only one of many possible sets of data that could have been observed.
- Understand the context of your datasetâwhat is the background science and how were measurements taken (for example, survey questions or direct measures)? What are the limitations of the measurement tools used to collect the data? Are some data missing? Why?
- Be thoughtful in choosing summary statistics.
- Decide early which parts of your analysis are exploratory and which parts are confirmatory, and preregister7 your hypotheses, if not formally then at least in your own mind.
- If you use p-values,8 which can provide some evidence regarding statistical results, follow these principles:
- Report effect sizes and confidence intervals (CIs);
- Consider providing graphical evidence of predicted values or effect sizes to display for your audience the magnitude of differences furnished by the analysis;
- Report the number of tests you conduct (formal and informal);
- Interpret the p-value in light of your sample size (and power);
- Donât use p-values to claim that the null hypothesis of no difference is true; and
- Consider the p-value as, at best, only one source of evidence regarding your conclusion rather than the conclusion itself.
- Consider creating customized, simulation-based statistical tests for answering your specific question with your particular dataset.
- Use simulations to understand the performance of your statistical plan on datasets like yours and to test various assumptions.
- Read results with skepticism, remembering that patterns can easily occur by chance (especially with small samples), and that unexpected results based on small sample sizes are often wrong.
- Interpret statistical results or patterns in data as being consistent or inconsistent with a conceptual model or hypothesis instead of claiming that they reveal or prove some phenomenon or relationship (see Chapter 2 for an elaboration of this recommendation).
Statistical Software
Table of contents
- Cover
- Half-Title
- Series
- Title
- Copyright
- Contents
- Preface
- Acknowledgments
- Author Biography
- 1 Introduction
- 2 Review of Elementary Statistical Concepts
- 3 Simple Linear Regression Models
- 4 Multiple Linear Regression Models
- 5 The ANOVA Table and Goodness-of-Fit Statistics
- 6 Comparing Linear Regression Models
- 7 Indicator Variables in Linear Regression Models
- 8 Independence
- 9 Homoscedasticity
- 10 Collinearity and Multicollinearity
- 11 Normality, Linearity, and Interaction Effects
- 12 Model Specification
- 13 Measurement Errors
- 14 Influential Observations: : Leverage Points and Outliers
- 15 Multilevel Linear Regression Models
- 16 A Brief Introduction to Logistic Regression
- 17 Conclusions
- Appendix A: : Data Management
- Appendix B: : Using Simulations to Examine Assumptions of Linear Regression Models
- Appendix C: : Selected Formulas
- Appendix D: : User-Written R Packages Employed in the Examples
- References
- Index