Moving Forward in the Debate on Causal Indicators: Rejoinder to Comments

Click to increase image sizeClick to decrease image size

Notes

¹ No evidence is provided for this assertion. Indicators often vary, as for example in measures of depression or many other areas with competing scales.

² Though Widaman agrees that the distinction is important, he suggests that causal indicators not be used without suggesting an alternative approach.

³ Note that several of the comments (e.g., Howell, 2014) referred to latent variables as either reflective or causal. We do not share this view, nor did we make this claim in our original article. This is a property of the indicator not the latent variable.

⁴ For multidimensional concepts, each dimension is represented by a latent variable.

⁵ Concern for post hoc interpretations, most strongly voiced by Widaman (2014), is addressed in the next section.

⁶ We also note that McCoach and Kenny raise the important issue of empirical underidentification in their commentary, but they do so from a theory-driven perspective because they frame the issue as one of identification, not that the latent variable would “disappear” in an underidentified model.

⁷ Notice that this process does not suggest that a latent variable does not “exist.” If creating a depression measure using effect indicators, and one or more indicators are not relating to the latent variable as predicted by theory, this calls into question the validity of the indicator not the existence of the concept of depression.

⁸ Bollen and Ting (2000) show that it is sometimes possible to test underidentified causal indicator models and to compare them to effect indicator models.

⁹ For some concepts, attempts to do so run into the danger of changing the nature of the concept we wish to study. For example, Howell et al. (2007) recommends substituting objective SES indicators for subjective measures, and this changes the concept from “objective” SES to perceived SES. These different concepts can have different causes and consequences.

¹⁰ If two studies have one or more outcomes in common and one of these common outcomes scales the latent variable, we can detect problems with the causal indicators if their coefficients differ significantly across studies. If they do not significantly change, have the proper direction of effect, and are of sufficient magnitude, this is evidence in support of their validity.

¹¹ Note that the same assumption is made in higher-order factor analysis.

¹² This approach also appears in Hauser and Goldberger (1971, p. 100).