As referred to above, factor analysis is a statistical tool that can help determine dimensionality when it is used to test theory. In this section, we briefly consider an important, but not always recognized, distinction between two different types of factors that also pertain to the determination of dimensionality. In one case, the indicators of a factor are a set of items determined to represent the same construct. The items or indicators are not understood to represent different constructs from each other; each item is instead understood to be an expression of the construct represented by a factor. When that is true, the factor represents a definable, homogeneous construct (provisionally, of course, pending ongoing evaluation of the validity of the theory and the empirical research). Two individuals with the same score on the factor would be understood to have the same level of the construct. This case is often described in terms of latent variable theory (Bollen, 2002; Bollen & Lennox, 1991; Borsboom, Mellenbergh, & van Heerden, 2003). Although a complete review of latent variable models is beyond the scope
