Factor Scores

Factor Scores Explained

As a contrived example study, consider 200 individuals who rate themselves on six questionnaire items written to measure personality traits. The individuals rate on a 5-point scale the extent to which each statement (e.g., “I have many close friends,” “I do not get stressed-out easily”) applies to themselves. A common factor analysis is subsequently conducted on the ratings, and two factors are extracted. After the factors are rotated with an oblique transformation, they are labeled Extroversion and Emotional Stability. Factor scores for the 200 individuals can now be computed by regressing the six item scores onto the two factors. Common factors are often referred to as latent or unobservable because their scores must be derived through such a regression analysis based on the original items. The resulting regression weights are referred to as factor score coefficients, and they can be applied to the standardized item responses to compute the factor scores. For example, Extroversion factor scores may be computed as follows:

The values .45, .32, .72, and the rest are the factor score coefficients, which are standardized regression weights. Coefficients are computed for all six items, and their relative absolute magnitudes indicate that the first three items contribute most to the prediction of scores on the Extroversion factor, while the remaining three items contribute less (their weights are near zero). Item 5 contributes negatively to the computation of Extroversion factor scores in this example.

Now consider two individuals, Joe and Mary. If their standardized responses (i.e., their z scores) on the rating scale are placed in the equation, their Extroversion factor scores are as follows:

Since high scores on the rating scale indicate greater extroversion, Joe is found to be extroverted and Mary is introverted. The standardized Emotional Stability factor scores can be computed similarly:

The second numbers (e.g., .05, .01, −.03) in each product are the factor score coefficients for the Emotional Stability factor, and the first numbers are Joe's and Mary's z scores for the six items. The results indicate that Mary is slightly more emotionally stable than Joe. The same coefficients for both factors could similarly be used to compute factor scores for the remaining 198 individuals in the study.

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