Building a Theoretical Foundation for the Spline‐Mixed Model Connection

ABSTRACT In fitting a non‐parametric regression model, the spline‐mixed model connection is well known, which associates fitting of a penalised spline model with that of a linear mixed model. We establish a theoretical framework for justifying the spline‐mixed model connection, and study the asymptotic behaviour of the empirical best linear unbiased predictor of the regression mean and associated model parameters.