A multitrait-multimethod model with minimal assumptions

A new model of confirmatory factor analysis (CFA) for multitrait-multimethod (MTMM) data sets is presented. It is shown that this model can be defined by only three assumptions in the framework of classical psychometric test theory (CTT). All other properties of the model, particularly the uncorrelated-ness of the trait with the method factors are logical consequences of the definition of the model. In the model proposed there are as many trait factors as different traits considered, but the number of method factors is one fewer than the number of methods included in an MTMM study. The covariance structure implied by this model is derived, and it is shown that this model is identified even under conditions under which other CFA-MTMM models are not. The model is illustrated by two empirical applications. Furthermore, its advantages and limitations are discussed with respect to previously developed CFA models for MTMM data.

[1]  Rolf Steyer,et al.  Models of classical psychometric test theory as stochastic measurement models: Representation, uniqueness, meaningfulness, identifiability, and testability. , 1989 .

[2]  Neal Schmitt,et al.  Methodology Review: Analysis of Multitrait-Multimethod Matrices , 1986 .

[3]  M. Browne,et al.  The decomposition of multitrait-multimethod matrices. , 1984, The British journal of mathematical and statistical psychology.

[4]  M. Eid,et al.  Do you feel better or worse? The validity of perceived deviations of mood states from mood traits , 1999 .

[5]  H. Marsh,et al.  A new, more powerful approach to multitrait-multimethod analyses: Application of second-order confirmatory factor analysis. , 1988 .

[6]  H. Marsh,et al.  Identification with deficient rank loading matrices in confirmatory factor analysis: Multitrait-multimethod models , 1994 .

[7]  Herbert W. Marsh,et al.  Latent variable models of multitrait-multimethod data. , 1995 .

[8]  Stephen G. West,et al.  Structural equation models with non-normal variables: Problems and remedies , 1995 .

[9]  Donald W. Zimmerman.  Probability spaces, hilbert spaces, and the axioms of test theory , 1975 .

[10]  S. Fiske,et al.  Personality Research, Methods, and Theory : A Festschrift Honoring Donald W. Fiske , 1995 .

[11]  H. Marsh.  Confirmatory Factor Analyses of Multitrait-Multimethod Data: Many Problems and a Few Solutions , 1989 .

[12]  K. Widaman.  Hierarchically Nested Covariance Structure Models for Multitrait-Multimethod Data , 1985 .

[13]  Karl G. Jöreskog,et al.  Lisrel 8: User's Reference Guide , 1997 .

[14]  D. W. Zimmerman.  Test Theory With Minimal Assumptions , 1976 .

[15]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[16]  H W Marsh,et al.  Overcoming Problems in Confirmatory Factor Analyses of MTMM Data: The Correlated Uniqueness Model and Factorial Invariance. , 1992, Multivariate behavioral research.

[17]  R. P. McDonald,et al.  Evaluation of Measurement Instruments by Meta-Analysis of Multitrait Multimethod Studies. , 1992 .

[18]  R. Bagozzi.  Assessing Construct Validity in Personality Research: Applications to Measures of Self-Esteem , 1993 .

[19]  M. Mount,et al.  Psychometric properties of subordinate ratings of managerial performance. , 1984 .

[20]  D. A. Kenny,et al.  Correlation and causality , 1979 .

[21]  Paul E. Spector,et al.  Estimation Problems in the Block-Diagonal Model of the Multitrait-Multimethod Matrix , 1990 .

[22]  R. Cudeck.  Msultiplicative Models and MTMM Matrices , 1988 .

[23]  D. A. Kenny,et al.  Analysis of the multitrait^multimethod matrix by confirmatory factor analysis , 1992 .

[24]  D. Campbell,et al.  Convergent and discriminant validation by the multitrait-multimethod matrix. , 1959, Psychological bulletin.

[25]  Peter M. Bentler,et al.  EQS : structural equations program manual , 1989 .