02 – Nonlinearities & Categorical Independent Variables

Categorical Data Analysis (Soc 681) · Purdue University · Fall 2026

The lecture notes for this section of the course, with the Stata code and output for every example. This site contains all the material and code for the course. If you prefer the slides in PDF format and/or the Stata replication do-file, these can be downloaded at: lecture slides · replication code.

2.0 Nonlinear effects

  • In physics, a function is nonlinear if the outcome (y) is not simply the additive product of all of the causes (x’s)
    • This can happen because effects of continuous IVs are not constant
    • This can happen because some effects are contingent upon values of other IVs
  • In applied statistics, we usually distinguish between those two sources:
    • When effects of an IV are not constant we say the effect is nonlinear
      • E.g., The prediction line is not perfectly straight
    • When the effect of one IV is contingent on the effects of another IV, we say the effects are interactive (as opposed to additive)
  • Note everything above is in terms of effects. Linear regression models can—and often do—produce nonlinear effects. They often produce interactive effects. They can even produce nonlinear interactive effects
  • Linear regression coefficients are useful when the effects are linear and additive. But this is a very special case. When effects are nonlinear and/or interactive we need different methods of summarizing and interpreting effects

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