A Note on Testing Perfect Correlations in SEM

This article is concerned with the seemingly simple problem of testing whether latent factors are perfectly correlated (i.e., statistically indistinct). In recent literature, researchers have used different approaches, which are not always correct or complete. We discuss the parameter constraints required to obtain such perfectly correlated latent factors in the context of 4 commonly used models: (a) the oblique factor model, (b) the hierarchical factor model, (c) models in which the factors are predicted by a covariate, and (d) models in which the factors are predictors of a dependent variable. It is shown that the necessary constraints depend on the choice of scaling. We illustrate testing the indistinctiveness of factors with 2 real data examples.

[1]  Klaus Oberauer,et al.  The multiple faces of working memory: Storage, processing, supervision, and coordination , 2003 .

[2]  Patrick C. Kyllonen,et al.  Working memory is (almost) perfectly predicted by g , 2004 .

[3]  A. Jensen,et al.  The g factor , 1996, Nature.

[4]  D. Borsboom,et al.  Different Kinds of DIF: A Distinction Between Absolute and Relative Forms of Measurement Invariance and Bias , 2002 .

[5]  W. Meredith.  Measurement invariance, factor analysis and factorial invariance , 1993 .

[6]  J. Gustafsson,et al.  The Hierarchical Organization of Cognitive Abilities: Restoring General Intelligence Through the Use of Linear Structural Relations (LISREL). , 1987, Multivariate behavioral research.

[7]  L. Pulkkinen,et al.  Dimensions of executive functioning: Evidence from children , 2003 .

[8]  C. Dolan,et al.  Investigating Spearman's Hypothesis by Means of Multi-Group Confirmatory Factor Analysis , 2000, Multivariate behavioral research.

[9]  J. S. Long,et al.  Testing Structural Equation Models , 1993 .

[10]  O. Wilhelm,et al.  Working memory capacity - facets of a cognitive ability construct , 2000 .

[11]  A. Jensen,et al.  The g factor , 1996, Nature.

[12]  Patrick C. Kyllonen,et al.  Reasoning ability is (little more than) working-memory capacity?! , 1990 .

[13]  Ralf Schulze,et al.  Working-memory capacity explains reasoning abilityand a little bit more , 2002 .

[14]  David J. Therriault,et al.  A latent variable analysis of working memory capacity, short-term memory capacity, processing speed, and general fluid intelligence , 2002 .

[15]  Thomas J. Bouchard,et al.  Just one g: consistent results from three test batteries , 2004 .

[16]  J. Gustafsson.  A unifying model for the structure of intellectual abilities , 1984 .

[17]  J. H. Steiger.  When constraints interact: a caution about reference variables, identification constraints, and scale dependencies in structural equation modeling. , 2002, Psychological methods.

[18]  R. Engle,et al.  The generality of working memory capacity: a latent-variable approach to verbal and visuospatial memory span and reasoning. , 2004, Journal of experimental psychology. General.

[19]  M. J. Emerson,et al.  The Unity and Diversity of Executive Functions and Their Contributions to Complex “Frontal Lobe” Tasks: A Latent Variable Analysis , 2000, Cognitive Psychology.

[20]  L. Wolfle,et al.  The Three-Stratum Theory of Cognitive Abilities: Test of the Structure of Intelligence across the Life Span. , 1995 .