230107 UE EC: Modelling choices - Regression models for binary and categorical outcomes (2023S)

This course will provide participants with the detailed understanding and advanced skills needed to interpret the results of logistic regression models with binary, ordinal and multinomial outcome variables.

Many courses on statistical methods only briefly cover how to interpret the results of logistic regression models. However, the results of such models are more difficult to interpret and to present than those for OLS regression models. In particular, interpreting logistic regression results is not limited to looking at coefficients and standard errors: we need to go beyond the simple regression output to gain a full understanding of what our results mean. This course will provide researchers with the tools to make the most of their regression results and to present their results in the most effective way possible. The focus throughout this course will be on practical analysis rather than on statistical theory.

In the first sessions, we will begin with a review of binary logistic regression models. What is the statistical rationale for these models, and how do they differ from OLS models? This session will also provide a review of basic commands for Stata, with a particular focus on running binary logistic regression models. Then, we will consider the two easiest ways of interpreting the results of binary logistic regressions. We will discuss how to interpret regression coefficients and then move on to using the odds ratios interpretation of the results. After that, we will move on to interpreting binary logistic regression results using predicted probabilities. We will learn how to calculate predicted probabilities by hand. We will then cover the various ways in which Stata can help in the calculation of predicted probabilities.

In the second half, we will learn how to present regression results and predicted probabilities graphically. Advantages and disadvantages of presenting results using predicted probabilities will be discussed. We will then consider the importance of uncertainty and how this can be included in the presentation of predicted probabilities. We will learn how to use Stata to run simulations. Finally, we will consider the level at which we should set other variables when calculating predicted probabilities. We will also consider other topics related to the interpretation of logistic regression models. The focus will lie on diagnostic techniques and on measures of model fit.

We will also consider how to interpret interaction effects in (binary) logistic regression models as well as other discrete outcomes (ordinal and nominal variables). Here, results need to be presented particularly clearly and carefully for readers to understand results well.

This course is at an intermediate level, so some familiarity with OLS regression will be assumed.

By the end of this course, participants will be able to:
- interpret the results of binary, ordinal and multinomial logistic regression models using log odds, odds ratios and predicted probabilities,
- present these results as tables and graphs in ways suitable for general and specialist audiences,
- interpret interaction effects in the appropriate ways,
- distinguish different measures of model fit and include these in presentations of results,
- run straightforward diagnostic tests of their model,
- and use Stata to run and understand logistic regression models.