Factor analytic modeling of within person variation in score profiles

Mark L Davison, Se Kang Kim, Catherine Close

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


A profile is a vector of scores for one examinee. The mean score in the vector can be interpreted as a measure of overall profile height, the variance can be interpreted as a measure of within person variation, and the ipsatized vector of score deviations about the mean can be said to describe the pattern in the score profile. A within person pattern interpretation of orthogonal factor loadings is developed. A statistic is proposed to index the amount of within person variation accounted for by an orthogonal factor. The statistic can be used to determine whether a factor warrants a within person pattern interpretation. A factor model with a random coefficient intercept is proposed for the study of within person score patterns accounting for within person variation. Two examples, one involving items from the Life Orientation Test and the other involving subscales of the Strong Vocational Interest Inventory, illustrate application of the factor model with an intercept, the within person variation statistic, and the profile pattern interpretation of factor loadings. With empirical support from the examples, it is conjectured that theoretically important traits often manifest themselves through within person score patterns.

Original languageEnglish (US)
Pages (from-to)668-687
Number of pages20
JournalMultivariate Behavioral Research
Issue number5
StatePublished - 2009

Bibliographical note

Funding Information:
This work has been supported by Grant R305C050059 from the Institute of Education Sciences in the U.S. Department of Education. Our thanks to Albert Maydeu-Olivares and Sharon A. Sackett for providing the data in our examples and to the editor and two anonymous reviewers for their helpful comments.


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