Estimating optimal weights for compound scores: a Bayesian IRT approach

Abstract

A method is proposed for constructing indices as linear functions of variables such that the reliability of the index is maximized.Reliability is defined in the framework of latent variable modeling and optima weights of the components of the index are found by maximizing the posterior variance relative to the total latent variable variance.The latent variable model is estimated in a Bayesian framework using Markov chain Monte Carlo (MCMC) computational methods and credibility regions are obtained for the reliability and the weights.The procedure is demonstrated with simulated data and a real dataset pertaining to the 28-joint Disease Activity Score.