Factorization of person response profiles to identify summative profiles carrying central response patterns

A data matrix, where rows represent persons and columns represent measured subtests, can be viewed as a stack of person profiles, as rows are actually person profiles of observed responses on column subtests. Profile analysis seeks to identify a small number of latent profiles from a large number of person response profiles to identify central response patterns, which are useful for assessing the strengths and weaknesses of individuals across multiple dimensions in domains of interest. Moreover, the latent profiles are mathematically proven to be summative profiles that linearly combine all person response profiles. Since person response profiles are confounded with profile level and response pattern, the level effect must be controlled when they are factorized to identify a latent (or summative) profile that carries the response pattern effect. However, when the level effect is dominant but uncontrolled, only a summative profile carrying the level effect would be considered statistically meaningful according to a traditional metric (e.g., eigenvalue ≥ 1) or parallel analysis results. Nevertheless, the response pattern effect among individuals can provide assessment-relevant insights that are overlooked by conventional analysis; to achieve this, the level effect must be controlled. Consequently, the purpose of this study is to demonstrate how to correctly identify summative profiles containing central response patterns regardless of the centering techniques used on data sets. (PsycInfo Database Record (c) 2024 APA, all rights reserved).