On Fair Person Classification Based on Efficient Factor Score Estimates in the Multidimensional Factor Analysis Model

Since Hooker, Finkelman and Schwartzman (Psychometrika 74(3): 419-442, 2009) it is known that person parameter estimates from multidimensional latent variable models can induce unfair classifications via paradoxical scoring effects. The open question as to whether there is a fair and at the same time multidimensional scoring scheme with adequate statistical properties is addressed in this paper. We develop a theorem on the existence of a fair, multidimensional classification scheme in the context of the classical linear factor analysis model and show how the computation of the scoring scheme can be embedded in the context of linear programming. The procedure is illustrated in the framework of scoring the Wechsler Adult Intelligence Scale (WAIS-IV).