Can ordered logistic regression suffer from omitted variable bias?

Question

If I ran an ordered logistic regression, with say a couple of explanatory variables, is it possible that omitted variables can bias the categorical outcome of the dependent variable similar to how this can happen in an OLS regression with a continuous dependent variable?

Answer 1

The problem is, if anything, even worse with logistic regression.

With ordinary least squares regression, if a variable z is associated with outcome

the omitted-variable bias ... is non-zero if the omitted variable z is correlated with any of the included variables in the [design] matrix X. [Emphasis added.]

With other types of regressions, for example logistic and Cox regressions, you can get omitted-variable bias even if z isn't correlated with the included variables! This page provides an introduction with links for further reading, and an analytic demonstration of the result for the specific case of probit regression.

If z is uncorrelated with the included predictors, the bias in coefficient estimates for the included predictors will be toward lower magnitudes, toward zero. In many practical applications omitted variables will be correlated with included ones, so bias could be in any direction.