3E Introduction to Regression

Course Content

This course covers regression analysis, both with continuous, ordinal, and categorical dependent variables. The focus will be on applied regression analysis, yet we will also deal with related topic like data treatment in Stata, interpretations, and how to test regression assumptions. The course includes ordinary least squares regression, logistic, ordinal, and multinomial regression, how to model and interpret non-linear effects as well as different types of statistical interactions. We will also focus on how to deal with breaches of assumptions.

Course Objectives

The course will enable the students to perform a range of regression models, to work with data treatment, and to be able to critically evaluate and interpret different types of regression models.

Course Prerequisites

The students should have some knowledge about basic descriptive statistics, measures of central tendency and spread. It is also good to have some knowledge about the statistical software Stata. However, instruction and notes will be made available, so it is possible for everyone to follow (though you must work harder if you do not have previous knowledge). The course will, to a large degree, follow the structure of the book Applied Statistics using Stata. In the reading list are also included short Sage books from the series Quantitative Application in the Social Sciences that dwell deeper into the topics of logistic regression and missing data (note that these are not Stata-books but deals more with statistical theory). In the recommended readings section, I have included to Stata introduction books for those who are not very comfortable with this software (you only need one of these), as well as a book on dummy variables and some additional chapters in our main book.

Course material

The students will have access to lectures, computer lab assignments, and dataset. The former two are also available as video-recordings (links to the lectures and computer instructions will be provided). There will be one topic each day, with a combination of regular classroom teaching with a following computer lab for each lecture.

Be aware that even though the course is divided into 10 topics (one for each day), some topics require more work than others (especially topic #3).

Representative Background Reading (this text will be provided by ESS)

Mehmetoglu, Mehmet & Tor G. Jakobsen (2022). Applied Statistics using Stata: A Guide for the Social Sciences. Thousand Oaks, CA: Sage. Chapters: 2 & 3.

Required Texts

Allison, Paul D. (2002). Missing Data. Thousand Oaks, CA: Sage.

Pampel, Fred C. (2000). Logistic Regression: A Primer. Thousand Oaks, CA: Sage.

Mehmetoglu, Mehmet & Tor G. Jakobsen (2022). Applied Statistics using Stata: A Guide for the Social Sciences, 2^nd ed. Thousand Oaks, CA: Sage. Chapters: 1, 2, 3, 4, 5, 6, 7, 8 & 15.

Recommended Readings

Acock, Alan C. (2018). A Gentle Introduction to Stata, 6^th ed. College Station, TX: Stata Press.

Hardy, Melissa A. (1993). Regression with Dummy Variables. Thousand Oaks, CA: Sage.

Mehmetoglu, Mehmet & Tor G. Jakobsen (2022). Applied Statistics using Stata: A Guide for the Social Sciences. London: Sage. Chapters: 10 & 11

Part 1: Introduction to Stata, Research and Statistics

1. Research and statistics
2. Introduction to Stata

Part 2: Regression analysis

3. Bivariate regression
4. Multiple regression
5. Dummy-variable regression
6. Interaction effects
7. Assumptions and diagnostics
8. Logistic regression

Part 3: Advanced topics

9. Critical issues
10. Advanced topics

Background knowledge required

It is an introduction course, so a little background in e.g. Stata is an advantage, but not necessary (as the candidates will learn it during the course)

POTENTIAL ESS APPLICANTS ARE TO BE ADVISED THAT RECORDINGS WILL NOT BE MADE AVAILABLE FOR THIS COURSE.

Research and statistics

• Methodology
• Positivism
• Statistical method
• Regression analysis,
• Normal distribution
• Central limit theorem
• T-distribution
• Degrees of freedom (df)

Readings: Mehmetoglu & Jakobsen (2022): ch. 1

Introduction to Stata

• Commands and windows
• Generating and recoding
• Graphs
• Do-file
• Scale, OLS, logistic
• Punching your own data

Readings: Mehmetoglu & Jakobsen (2022): ch. 2

Bivariate regression

• Regression analysis
• Bivariate regression
• Error term
• Regression analysis/OLS
• Predicting in linear regression
• Standard error
• Hypothesis testing
• Confidence intervals
• R-squared

Readings: Mehmetoglu & Jakobsen (2022): ch. 3

Multiple regression

• Multiple regression
• F-test
• Adjusted R²
• Partial slope coefficients
• Standardization and relative importance

Readings: Mehmetoglu & Jakobsen (2022): ch. 4

Dummy variable regression

• Dichotomous variable
• Dummy set

Readings: Mehmetoglu & Jakobsen (2022): ch. 5;

Interaction effects

• Product-term approach
• Continuous predictor and dummy moderator
• Continuous predictor and polytomous moderator
• Dummy predictor and dummy moderator
• Continuous predictor and continuous moderator

Readings: Mehmetoglu & Jakobsen (2022): ch. 6

Assumptions and diagnostics

• The assumptions
• Correct specification of the model
• Assumptions about the residuals
• Influential observations

Readings: Mehmetoglu & Jakobsen (2022): ch. 7

Logistic regression

• What is logistic regression?
• Assumptions of logistic regression
• Example of logistic regression
• Diagnostics
• Multinomial logistic regression
• Ordered logit regression

Readings: Mehmetoglu & Jakobsen (2022): ch. 8; Pampel (2000)

Critical issues

• Skewness and kurtosis
• Transformation of variables
• Weighting cases

Readings: Mehmetoglu & Jakobsen (2022): ch. 15

Advanced topics

• Interaction with non-linear predictor
• Missing data

Readings: Mehmetoglu & Jakobsen (2022): ch. 15, Allison (2002)