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Statistics in a Nutshell by Sarah Boslaugh, Paul Andrew Watters

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Chapter 15. Other Types of Regression

In Chapter 14, you learned about multiple linear regression. Although multiple linear regression is appropriate for many scenarios, other types of regression, including logistic and nonlinear, are best used under different circumstances. This chapter reviews scenarios in which these types of regression are the correct analytic choice, and covers how to perform these analyses, the meaning of the results, and issues to be wary of, such as overfitting.

Logistic Regression

In Chapter 14, multiple linear regression was presented as regressing a real-valued DV on two or more IVs, measured on interval or ratio scales, or categorical IVs, coded using binary variables. Logistic regression is commonly used when the DV is also categorical, typically nominal. Logistic regression is commonly used in epidemiological studies to understand the relationship between a number of risk factors (categorical or real-valued) and a categorical DV. For example, while it may be possible to use a real-valued DV from which hypertension can be deduced, a clinician is typically interested in making a diagnosis (hypertensive/not hypertensive) based on several different IVs. The reason that you need logistic regression is that the assumption of common variance in the DV is not met when the two possible values are 0 and 1. Also, any linear regression model may predict DV values less than 0 or greater than 1, which would have no meaning in terms of the nominal codings for categories. ...

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