Parametric model measurement: reframing traditional measurement ideas in neuropsychological practice and research.

Objective: Neuropsychology is an applied measurement field with its psychometric work primarily built upon classical test theory (CTT). We describe a series of psychometric models to supplement the use of CTT in neuropsychological research and test development.
Method: We introduce increasingly complex psychometric models as measurement algebras, which include model parameters that represent abilities and item properties. Within this framework of parametric model measurement (PMM), neuropsychological assessment involves the estimation of model parameters with ability parameter values assuming the role of test 'scores'. Moreover, the traditional notion of measurement error is replaced by the notion of parameter estimation error, and the definition of reliability becomes linked to notions of item and test information. The more complex PMM approaches incorporate into the assessment of neuropsychological performance formal parametric models of behavior validated in the experimental psychology literature, along with item parameters. These PMM approaches endorse the use of experimental manipulations of model parameters to assess a test's construct representation. Strengths and weaknesses of these models are evaluated by their implications for measurement error conditional upon ability level, sensitivity to sample characteristics, computational challenges to parameter estimation, and construct validity.
Conclusion: A family of parametric psychometric models can be used to assess latent processes of interest to neuropsychologists. By modeling latent abilities at the item level, psychometric studies in neuropsychology can investigate construct validity and measurement precision within a single framework and contribute to a unification of statistical methods within the framework of generalized latent variable modeling.