Mixture regression with shared slopes ($Y_i\mid Z_i=j,x_i\sim N({\alpha }_j+x_i^T\beta ,{\sigma }^2)$)

A mixture regression with shared slopes models $Y_i\mid Z_i=j,x_i\sim N({\alpha }_j+x_i^T\beta ,{\sigma }^2)$ with common slopes and component-specific intercepts. It jointly estimates mean adjustment and latent groups, rather than fitting a mixture to fixed residuals. If both a global intercept and component offsets are included, an identifying constraint is required. Constant weights assume latent membership proportions do not depend on the covariates.