A tutorial on regression-based norming of psychological tests with GAMLSS

A norm-referenced score expresses the position of an individual test taker in the reference population, therebyenabling a proper interpretation of the test score. Such normed scores are derived from test scores obtainedfrom a sample of the reference population. Typically, multiple reference populations exist for a test, namelywhen the norm-referenced scores depend on individual characteristic(s), as age (and sex). To derive normedscores, regression-based norming has gained large popularity. The advantages of this method over traditionalnorming are its flexible nature, yielding potentially more realistic norms, and its efficiency, requiringpotentially smaller sample sizes to achieve the same precision. In this tutorial, we introduce the reader toregression-based norming, using the generalized additive models for location, scale, and shape (GAMLSS).This approach has been useful in norm estimation of various psychological tests. We discuss the rationale ofregression-based norming, theoretical properties of GAMLSS and their relationships to other regression-basednorming models. Based on 6 steps, we describe how to: (a) design a normative study to gather propernormative sample data; (b) select a proper GAMLSS model for an empirical scale; (c) derive the desirednormed scores for the scale from the fitted model, including those for a composite scale; and (d) visualize theresults to achieve insight into the properties of the scale. Following these steps yields regression-based normswith GAMLSS for a psychological test, as we illustrate with normative data of the intelligence test IDS-2.
ThecompleteRcode and data set is provided as online supplemental material.