Ways to Treat Single-Indicator Variables

(Updated April 17, 2018)

Often, a researcher will have one or more single-indicator variables within his or her model. It could be a demographic variable such as gender or age, or a total scale score for some social/psychological questionnaire (e.g., Rosenberg Self-Esteem Scale).

With multiple manifest indicators for a latent construct, the construct is automatically rendered "error-free," with measurement error segregated out into each indicator's residual "tiny bubble." Relations between constructs will be stronger when they are error free. Single-indicator variables, when left to stand alone, usually have measurement error, but are assumed to be perfectly measured.

Here are five scenarios in which a researcher was interested in studying self-esteem (thanks to CRO for the photograph of the board).

As shown in the photo, reliability-corrected single-indicator constructs are a way to account for measurement error in single-indicator variables (lower-right). The following is a quote from Choi et al. (2011): “To account for imperfect reliability of the scale scores, we created latent variables to represent the … constructs with each latent variable being measured by its corresponding scale score and the residual variance of the scale score fixed to (1-scale reliability) * scale variance (Hayduk, 1987).” Cronbach's alpha (internal consistency) is often used as the reliability value. A made-up example of this procedure is shown in the photo.

I previously created the following graphic to illustrate further the difference between keeping single variables as they are and using reliability correction.

NEW! Video of Todd Little speaking at Texas Tech about parceling (February 2, 2018). Follow this link to the video (limited to TTU); listed under Daniel Bontempo, organizer of IMMAP series.

References and Resources

Choi, K. H., Bowleg, L., & Neilands, T. B. (2011). The effects of sexism, psychological distress, and difficult sexual situations on U.S. women's sexual risk behaviors. AIDS Education and Prevention, 23(5), 397-411. (LINK)

Cole, D. A., & Preacher, K. J. (2014). Manifest variable path analysis: Potentially serious and misleading consequences due to uncorrected measurement error. Psychological Methods, 19, 300-315. (LINK)

Hayduk L. A. (1987). Structural equation modeling with LISREL: Essentials and advances. Baltimore, MD, USA: Johns Hopkins University Press.