Factor Analytic Modeling of Within Person Variation in Person Profiles of Observed Scores

What is it about?

A profile is an array of scores for one examinee. The mean score in the profile can be interpreted as a measure of overall profile height; the variance can be interpreted as a measure of within person variation; and the score deviations around the mean can be said to describe the pattern in the person 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 subscores 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.

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Why is it important?

The magnitudes and directions of orthogonal factor loadings were interpreted as the most typical (or core) profile patterns and relevant factor scores functioned as matching statistics between person profiles (observed scores) and core profiles depicted by the orthogonal factor loadings.

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