Residual mixture clustering

Residual mixture clustering first removes a fitted covariate-dependent mean and then explores latent groups in the regression residuals. It seeks differences relative to the adjustment rather than raw-response differences. Mixture responsibilities express uncertain membership. The fitted mixture alone does not establish distinct real-world populations, and two-stage residual mixture fitting ignores some adjustment uncertainty.

Fitting a mixture model to regression residuals treats the fitted mean adjustment as fixed. Even with independent homoscedastic errors, ordinary least-squares residuals have covariance matrix ${\sigma }^2(I-H)$ and satisfy fitted linear constraints, so they are not exactly independent observations. A joint mixture regression with shared slopes or a bootstrap of the whole fitting process better accounts for the first-stage estimation uncertainty.