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This study aims to reparameterize ordinary factors into between- and within-person factor effects and utilize an array of the within-person factor loadings as a latent profile which encapsulates all score responses of individuals in a population. To illustrate, the Woodcock–Johnson III (WJ-III) tests of cognitive abilities were analysed and one between- and two within-person factors were identified. The scoring patterns of individuals in the WJ-III sample were interpreted according to the within-person factor patterns. Regression analyses were performed to examine how much the within-person factors accounted for the person scoring patterns and criterion variables. Finally, the importance and applications of the between- and within-person factors are discussed.