The insidious effects of failing to include design-driven correlated residuals in latent-variable covariance structure analysis.

Bibliographic Data

ID23349877
AuthorsDavid A Cole (0000-0002-7535-1230, Vanderbilt University), Jeffrey A Ciesla (0000-0002-2635-3061, Vanderbilt University), James H Steiger (Vanderbilt University)
Year2007
Volume12
Issue4
Pages381-398
Publication date2007-12-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenuePsychological Methods (JOURNAL)
Journal identifiersISSN: 1082-989X • E-ISSN: 1939-1463
PublisherAmerican Psychological Association (APA) (PUBLISHER)
DOI10.1037/1082-989x.12.4.381
PMID18179350
OpenAlexW2002538709
LanguageEN
Citations received105
References cited14

In practice, the inclusion of correlated residuals in latent-variable models is often regarded as a statistical sleight of hand, if not an outright form of cheating. Consequently, researchers have tended to allow only as many correlated residuals in their models as are needed to obtain a good fit to the data. The current article demonstrates that this strategy leads to the underinclusion of residual correlations that are completely justified on the basis of measurement theory and research design. In many designs, the absence of such correlations will not substantially harm the fit of the model; however, failure to include them can change the meaning of the extracted latent variables and generate potentially misleading results. Recommendations include (a) returning to the full multitrait-multimethod design when measurement theory implies the existence of shared method variance and (b) abandoning the evil-but-necessary attitude toward correlated residuals when they reflect intended features of the research design.

Analysis of covariance · Cheating · Covariance · Econometrics · Economics · Harm · Latent variable · Latent variable model · Residual · Statistics · Structural equation modeling · Variable (mathematics) · Variance (accounting) · Advanced Statistical Methods and Models · Advanced Statistical Modeling Techniques · Mathematics · Psychology · Psychometric Methodologies and Testing · Social Psychology