Model Selection in Continuous Test Norming With GAMLSS.

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Continuous norming is preferred over traditional methods for computing norms from reference group test scores.
• The Box-Cox Power Exponential model within generalized additive models for location, scale, and shape is suitable for continuous norming.
• Automatic model selection for the Box-Cox Power Exponential model in test norming requires investigation.

Purpose of the Study:

• To evaluate the performance of automatic model selection procedures for the Box-Cox Power Exponential model in test norming.
• To compare different model-fit criteria in conjunction with stepwise selection methods.
• To identify the most efficient model selection procedure for continuous norming.

Main Methods:

• A simulation study was conducted comparing two stepwise model selection procedures.
• Four model-fit criteria were evaluated: Akaike information criterion, Bayesian information criterion, generalized Akaike information criterion (3), and cross-validation.
• Data complexity, sampling design, and sample size were varied in a fully crossed design.

Main Results:

• A novel stepwise model selection procedure combined with the generalized Akaike information criterion demonstrated superior efficiency.
• This advocated procedure required the smallest sample size for effective model selection.
• The performance of different model-fit criteria varied depending on data complexity and sample size.

Conclusions:

• The proposed model selection procedure offers an efficient approach for applying the Box-Cox Power Exponential model in continuous norming.
• This method is practical for test norming, as demonstrated with intelligence test data.
• Accurate model selection is crucial for reliable norm computation in psychometrics.