Model Selection in Continuous Test Norming With GAMLSS

To compute norms from reference group test scores, continuous norming is preferred over traditional norming. A suitable continuous norming approach for continuous data is the use of the Box-Cox Power Exponential model, which is found in the generalized additive models for location, scale, and shape. Applying the Box-Cox Power Exponential model for test norming requires model selection, but it is unknown how well this can be done with an automatic selection procedure. In a simulation study, we compared the performance of two stepwise model selection procedures combined with four model-fit criteria (Akaike information criterion, Bayesian information criterion, generalized Akaike information criterion (3), cross-validation), varying data complexity, sampling design, and sample size in a fully crossed design. The new procedure combined with one of the generalized Akaike information criterion was the most efficient model selection procedure (i.e., required the smallest sample size). The advocated model selection procedure is illustrated with norming data of an intelligence test.