Evaluating Effect, Composite, and Causal Indicators in Structural Equation Models

Abstract

Although the literature on alternatives to effect indicators is growing, there has been little attention given to evaluating causal and composite (formative) indicators. This paper provides an overview of this topic by contrasting ways of assessing the validity of effect and causal indicators in structural equation models (SEMs). It also draws a distinction between composite (formative) indicators and causal indicators and argues that validity is most relevant to the latter. Sound validity assessment of indicators is dependent on having an adequate overall model fit and on the relative stability of the parameter estimates for the latent variable and indicators as they appear in different models.If the overall fit and stability of estimates are adequate, then a researcher can assess validity using the unstandardized and standardized validity coefficients and the unique validity variance estimate. With multiple causal indicators or with effect indicators influenced by multiple latent variables, collinearity diagnostics are useful. These results are illustrated with a number of correctly and incorrectly specified hypothetical models.

Convergent and Discriminant Validity with Formative Measurement: A Mediator Perspective

“…Previous studies have paid little attention to convergent and discriminant validity of formative measurement (Bollen, 2011). This may be attributed to the fact that formative measurement is quite different from reflective measurement.…”

“…As Bollen (2011) illustrated, formative measurement may include causal indicators or formative indicators. The key difference between these two types of indicators is that "causal indicators should have conceptual unity in that all the variables should correspond to the definition of the concept whereas formative indicators are largely variables that define a convenient composite variable where conceptual unity is not a requirement" (Bollen, 2011, p. 360).…”

“…Variables consisting of formative indicators may not have any meaningful conceptualization. Therefore, formative measurement with causal indicators is focused upon in this study (Bollen, 2011).…”

“…Furthermore, correlations among causal indicators within a measurement model need not be higher compared to correlations between them and indicators from other measurement models (Bollen, 2011;Bollen & Lennox, 1991). Therefore, the traditional approach toward establishing convergent and discriminate validity from CTT is not appropriate.…”

Pride and Prejudice and Causal Indicators

“…However, the theoretical arguments presented in such work seem to have had little impact on either the common use of causal / formative indicators in practice, nor the continuing proliferation of methodological articles defending their use (e.g. Bollen, 2007Bollen, , 2011Bollen and Bauldry, 2011;Bollen and Diamantopoulos, 2015;Diamantopoulos, 2011;Diamantopolous, Riefler, and Roth, 2008). It should be no surprise that we hope that the approach used in ARM2016 proves more convincing evidence to scholars that there are significant dangers in applying the causal / formative approach to measurement.…”