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, thereby enabling a proper interpretation of the test score. Such normed scores are derived from test scores obtained from a sample of the reference population. Typically, multiple reference populations exist for a test, namely when the norm-referenced scores depend on individual characteristic(s), as age (and sex). To derive normed scores, regression-based norming has gained large popularity. The advantages of this method over traditional norming are its flexible nature, yielding potentially more realistic norms, and its efficiency, requiring potentially smaller sample sizes to achieve the same precision. In this tutorial, we introduce the reader to regression-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 of regression-based norming, theoretical properties of GAMLSS and their relationships to other regression-based norming models. Based on 6 steps, we describe how to: (a) design a normative study to gather proper normative sample data; (b) select a proper GAMLSS model for an empirical scale; (c) derive the desired normed scores for the scale from the fitted model, including those for a composite scale; and (d) visualize the results to achieve insight into the properties of the scale. Following these steps yields regression-based norms with GAMLSS for a psychological test, as we illustrate with normative data of the intelligence test IDS-2. The complete R code and data set is provided as online supplemental material.

Automated summary

Norm-referenced scores are used to position individuals within a reference population, often depending on individual characteristics such as age and sex. Regression-based norming is preferred over traditional methods due to its flexibility, realistic norms, and efficiency in achieving precision with smaller sample sizes. Using generalized additive models can help in deriving normed scores for psychological tests, as demonstrated with intelligence test IDS-2 normative data provided in the tutorial.