Formative Constructs Implemented via Common Factors

Abstract

Recently there has been a renewed interest in formative measurement and its role in properly specified models. Formative measurement models are difficult to identify, and hence to estimate and test. Existing solutions to the identification problem are shown to not adequately represent the formative constructs of interest. We propose a new two-step approach to operationalize a formatively measured construct that allows a closely matched common factor equivalent to be included in any structural equation model. We provide an artificial example and an original empirical study of privacy to illustrate our approach. Detailed proofs are given in an appendix.

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Corrigendum

Notes

¹Other views of LVs are possible. Bollen (2002) provides an excellent overview.

²In early terminology, “formative” measurement did not require a disturbance term, whereas the phrase “causal indicator” is meant to permit but not require the disturbance. Issues regarding this disturbance term are summarized in Diamantopoulos (2006) and Wilcox et al. (2008).

³ Figure 1 appears to show that F is an independent variable, but it is in fact a dependent variable via F = P + D. The notation with V, F, E, and D is that of EQS (Bentler, 2006).

⁴This problem also pertains to reflective measurement, but with less severity. As Howell et al. (2007b) stated “No, reflective measures are not immune from contamination and potential interpretational confounding when estimated in a larger structural equation model. However, reflective models have epistemic relationships that exist independently from structural relationships” (p. 208). See also Kim et al. (2010).

⁵A simple example from Bollen (2002) might help. He suggested “time spent with friends, time spent with family, and time spent with coworkers as indicators of the [formative] latent variable of time spent in social interaction” (p. 616). If the indicators are V ₁, V ₂, and V ₃, and P = V ₁ + V ₂ + V ₃, we could take P ₁ = V ₁ + V ₂ and P ₂ = V ₃.