Week 7: Dichotomous Predictors, Non-Linearity, and Data Transformations (02/22/2024)

Ozlem Tuncel

otuncelgurlek1@gsu.edu

⚠️ CAUTION: DO NOT SOLELY RELY ON MY NOTES. THERE MIGHT BE TYPOS AND MISTAKES.

✔️ The goal of this week is to learn about binary independent variables and data transformations.

Here are some key points:

• Substantive meaning: clearly describe the effect that you observe on your regression result.
• We can use interval and ratio as DV in OLS (and if we have enough number of categories, ordinal can be also used)
• We can use factors, ordinal, interval, and ratio as independent variables. But, when using factors (binary variable), be careful about interpretation.
• Dichotomous, dummy, factor, binary, indicator - these are all the same thing!
• Use 0 and 1 for binary variables – 1 representing the theoretical interest. Make sure to meaningfully name your variables.
• Notational D is a vector of binary variables
• “Expected values of Y for D (i.e., male) is …” This is how we interpret dichotomous variables.
• Reference category = baseline category
• Since $D_l$ are mutually exclusive and exhaustive, we need to omit the “reference category” or $\beta_0$ (due to perfect multicollinearity)
• If we omit the reference the category, it becomes the baseline, and we can interpret using the comparison with the baseline.
• How to choose a reference cateogry? Either there is natural neutral category in your variable (i.e., Independents, Neutral). Or, my theory can give a me a meaningful category to pick as a reference. If you do not have any guidence from theory, use the modal category (mode of the variable).
• Higher order transformations (e.g., squares) inflates high numbers and compresses small numbers; and lower-order transformations (e.g., logs) compresses large values and inflates smaller ones.
• $\forall$ means “for all” and $s.t.$ means “such that”

Some suggestions:

• Want to learn more about factors in R, see this
• See Figure 15.14 in this chapter, if you are curious about how logistic regression looks like in 3D.
• Read more about binary variables and intercept shift here
• John Fox’s recommendations for monotonic transformations
• How to interpret your findings when you used log() in our variables? Here is a great source