Getting to clustered standard errors for Multinomial Logit models
Starting from scratch — the geometry of ℝⁿ, through OLS standard errors under homoskedasticity, then heteroskedasticity, clustering, and finally the multinomial logit. Each part builds directly on the last.
Part 1: The geometry in ℝⁿ, math and intuition of OLS and standard errors under homoskedasticity
May 2026Y is a point in ℝⁿ. col(X) is a subspace. OLS projects Y onto it. Everything — β̂, σ̂², standard errors, degrees of freedom — follows from that single geometric fact.
Part 2: Heteroskedasticity and robust standard errors
May 2026Dropping the equal-variance assumption. The true variance of β̂ becomes a sandwich — (XᵀX)⁻¹XᵀΩX(XᵀX)⁻¹. How to estimate it, why leverage matters, and the HC0–HC3 corrections.