The restricted maximum likelihood method for variance estimation in a mixed model with additive penalized-spline

Abstract

Estimation of variance components in the model often needed in the problem of model-based prediction. We present the concept of restricted maximum likelihood estimation for variance components in the mixed model with additive p-spline. We provide simulations as a result of applying the REML estimator concept to variance components in diverse models with p-spline additives. The model is then used to predict the means of sub-area of the population. The limited simulation shows the performance of the model using the REML estimator for the variance component to provide better predictive results, indicated by the average RMSPE value and smaller absolute average values and the denser distribution of the MSPE with a lower median, than that produced by the model the same as the ML estimator for component variance.