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.
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.
