What is a factor score?
A factor score is a numerical value that indicates a person's relative spacing or standing on a latent factor. In order to develop this definition further, however, we must draw a distinction that grew out of the indeterminacy debate between "factor scores" and "factor score estimates". The former scores fulfill the stipulations of the common factor model exactly and are not encountered in applied uses of factor analysis; rather, in practice (for example, in the published literature or in leading statistical software) one encounters factor score estimates, which are imperfect representations of the factors that do not fulfill the stipulations of the common factor model. In other words, factor score estimates are not perfectly correlated with the factors themselves, and depending on the nature of a particular data set these estimates may in fact only be moderately correlated with the factors.
Why do we compute factor score estimates in the first place? Why not compute proper factor scores? Factor scores can in fact be computed and it is a myth to state that, "factor scores cannot be computed, they can only be estimated." To explain why factor score estimates -- rather than factor scores -- are computed in practice, we must draw another distinction between the "indeterminate" and "determinate" portions of factor scores. The indeterminate portion of a particular factor score is essentially a random number that is added to the determinate portion of the same factor score. Two researchers who wish to compute factor scores on an indeterminate factor would agree on the determinate portions of the scores, but could use very different values for the indeterminate portions. As explained under "What is factor score indeterminacy?" both researchers would still be able to construct sets of factor scores that are equally consistent with the pattern coefficients representing the extracted factor. In other words, both sets of factor scores would satisfy the stipulations of the common factor model. In practice, however, researchers attempt to focus on the determinate portion of the factor scores while ignoring the indeterminate (random) portion. Thurstone's original method of estimating factor scores in fact maximized the degree of determinacy. Because the factor score estimates are not computed from both determinate and indeterminate portions, however, they will not be perfectly valid indicators of the factors they are intended to measure and they will not satisfy the stipulations of the common factor model. As suggested above, depending on a number of different conditions, the factor score estimates may in fact stand as poor representations of the factors themselves. It is therefore extremely important that researchers evaluate the properties of their factor score estimates.
Rephrasing the title question above
to "What is a factor score estimate?", yields a very similar answer.
Specifically, "a factor score estimate is a numerical value that is meant
to indicate a person's relative spacing or standing on a latent factor."
Typically, factor score estimates are computed and reported in approximately
standardized form. For example, consider a factor labeled “extraversion
/ introversion.” A person with a factor score of 2.03 is rather extreme
on the extraversion end of the factor compared to a person who is slightly
introverted with a score of -.20. These approximately standardized estimates
are often obtained from leading statistical programs such as SPSS or SAS
and will be referred to as "Refined Factor Score Estimates" or simply "Refined
Factor Scores" throughout these web pages.
Factor score estimates are also encountered as simple sum scores computed from ability measures, clinical scales, personality questionnaires, etc. that have been constructed using factor analytic methodology. The index scores on the WISC-III or the facet scores from the NEO PI-r, for example, are computed by summing different subscale scores or item responses, respectively. These sums are considered as factor score estimates because they are values intended to indicate a person's relative spacing (or at least ranking) on the latent factors of interest (e.g., processing speed or neuroticism). These factor score estimates will be referred to as "Coarse Factor Score Estimates" or simply "Coarse Factor Scores" throughout these web pages. Compared to the refined factor scores, the coarse factor scores are easier to compute and will almost invariably be whole numbers with known ranges.