Offending estimates in covariance structure analysis: Comments on the causes of and solutions to Heywood cases.

Abstract

In this article we discuss, illustrate, and compare the relative efficacy of three recommended approaches for handling negative error variance estimates (i.e., Heywood cases): (a) setting the offending estimate to zero, (b) adopting a model parameterization that ensures positive error variance estimates, and (c) using models with equality constraints that ensure nonnegative (but possibly zero) error variance estimates. The three approaches are evaluated in two distinct situations: Heywood cases caused by lack of fit and misspecification error, and Heywood cases induced from sampling fluctuations. The results indicate that in the case of sampling fluctuations the simple approach of setting the offending estimate to zero works reasonably well. In the case of lack of fit and misspecification error, the theoretical difficulties that give rise to negative error variance estimates have no ready-made methodological solutions.

Cites (30)

1. Modern factor analysis
   Harry H. Harman · 1960
2. Factor Analysis as a Statistical Method.
   Basilevsky, A., Lawley, D. N., Maxwell, A. E. · 1972 · The Statistician
3. Correlation and causality
   David A. Kenny · 1979 · Medical Entomology and Zoology
4. Attitudes towards objects as predictors of single and multiple behavioral criteria.
   Fishbein, Martin, Ajzen, Icek · 1974 · Psychological Review
5. Models of attitude-behavior relations.
   P. M. Bentler, George Speckart · 1979 · Psychological Review
6. Statistical Inference in Factor Analysis
   T. W. Anderson, Herman Rubin · 1956 · Project Euclid (Cornell University)
7. Attitudes, intentions, and behavior: A test of some key hypotheses
   Bagozzi, Richard P. · 1981 · Journal of Personality and Social Psychology
8. Some Contributions to Maximum Likelihood Factor Analysis
   Jöreskog, K. G. · 1967 · Psychometrika
9. Factor Analysis as a Statistical Method.
   Browne, M. W., Lawley, D. N., Maxwell, A. E. · 1973 · Journal of the American Statistical Association
10. Linear Structural Equations with Latent Variables
    Bentler, P. M., Weeks, David G. · 1980 · Psychometrika

Show all 30 references

Cited by (26)

1. Structural equation modeling in practice: A review and recommended two-step approach
   Anderson, James C., Gerbing, David W. · 1988 · Psychological Bulletin
2. Using PLS Path Modeling for Assessing Hierarchical Construct Models: Guidelines and Empirical Illustration1
   Wetzels, Martin, Odekerken-Schröder, Gaby, van Oppen, Claudia · 2009 · MIS Quarterly
3. Lack of method variance in self-reported affect and perceptions at work: reality or artifact?
   Williams, Larry J., Cote, Joseph A., Buckley, M. Ronald · 1989 · Journal of Applied Psychology
4. Is More Ever Too Much? The Number of Indicators per Factor in Confirmatory Factor Analysis
   Marsh, Herbert W., Hau, Kit-Tai, Balla, John R., Grayson, David · 1998 · Multivariate Behavioral Research
5. Affects of variable and subject sampling on factor pattern recovery.
   Velicer, Wayne F., Fava, Joseph L. · 1998 · Psychological Methods

See all 337