Identifying between‐person and within‐person factors to enhance understanding of observed score profiles

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.