Commentary: Theoretical Equivalence, Measurement Invariance, and the Idiographic Filter

Nesselroade, Gerstorf, Hardy, and Ram (this issue) propose to "filter out" idiosyncrasies of dynamic processes at the level of the individual through the application of dynamic factor analysis. The problem that they deal with is that individuals may differ in the items that are "salient" for a given construct, so that the same measurement model does not hold across subjects. The proposed method, however, allows for the same constructs to be measured by different items in different subjects, and therefore appears to bypass this problem. Nesselroade et al. accomplish this by first estimating a dynamic factor model for each individual, where the item-factor relations are free to vary across subjects, and then executing a higher order analysis in which the factor intercorrelations are required to be identical across subjects. They motivate this procedure partly by appealing to the literature on measurement invariance; the only difference, in their own words, is that they define "invariance at the level of construct interrelations rather than at the level of construct-observables relations."