Shared-parameter model for informative dropout ($\int f(Y_i\mid B_i,X_i)g(R_i\mid B_i,X_i)dF(B_i)$)

A response model and a dropout model share latent random effects. Conditional on those effects and observed predictors, the two processes may be independent, yet marginally dropout is missing not at random because the shared effects also predict unseen outcomes. Joint likelihood fitting integrates the product of both models over the shared effects; integrating the outcome model alone is insufficient. This is an explicit identifying model, and its latent-dependence assumptions should be assessed by sensitivity analysis.