 Errors-in-variables model

An errors-in-variables model distinguishes a latent true predictor from its noisy measurement and models both the measurement and the response. For example, $W_i\mid U_i\sim N(U_i,s^2)$ and $Y_i\mid U_i\sim N(a+b{U}_i,v^2)$, with a population distribution for $U_i$, propagate predictor uncertainty into inference on $b$. Treating $W_i$ as exact can create attenuation bias from classical measurement error. Identifiability requires appropriate information about the measurement process or latent predictor distribution.