Factor Analytic Modeling of Within Person Variation in Score Profiles

Abstract

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.

Notes

*p < .05.

**p < .01.

^aOf the variance accounted for by the factor, the % that is within person variation; the % within and % between will sum to 100%.