Multitrait-Multimethod Comparisons Across Populations: A Confirmatory Factor Analytic Approach.

The advantages of multitrait-multimethod (MTMM) methodology and the power of maximum likelihood confirmatory factor analysis are combined in an ordered framework for the comparison of covariance structures and true means across populations. First, a sequence of tests of and between hierarchically nested confirmatory factor analytic models is described for the analysis of measurement equivalence and construct validity across populations. Second, a similar sequence of model comparisons is proposed for the detection of true score-observed score regression intercept differences and true mean differences between populations. The proposed procedure is contrasted with MANOVA comparisons of group means: (1) use of MANOVA assumes test equivalence and validity across populations, whereas the present procedure permits statistical analysis of these assumptions; (2) MANOVA bases discriminant function coefficients partially upon observed differences between groups, whereas the current procedure weights each variate according to its correlation with an underlying construct. The possibility of spurious results from MANOVA and verdical results from the proposed methodology is demonstrated via application of both procedures to an artificial data set.

[1]  L. Cronbach,et al.  Construct validity in psychological tests. , 1955, Psychological bulletin.

[2]  Robert L. Linn,et al.  Path analysis: Psychological examples. , 1970 .

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

[4]  A. Goldberger,et al.  Structural Equation Models in the Social Sciences. , 1974 .

[5]  K. Jöreskog.  A general approach to confirmatory maximum likelihood factor analysis , 1969 .

[6]  K. Jöreskog,et al.  Analysis of linear structural relationships by maximum likelihood, instrumental variables, and least sqsuares methods , 1986 .

[7]  K. Schaie,et al.  The organization of spatial abilities in older men and women. , 1977, Journal of Gerontology.

[8]  S. Mulaik,et al.  Single-sample tests for many correlations. , 1977 .

[9]  E. Labouvie,et al.  Identity versus equivalence of psychological measures and constructs. , 1980 .

[10]  J. Neter,et al.  Applied linear statistical models : regression, analysis of variance, and experimental designs , 1974 .

[11]  W. R. Cunningham,et al.  Principles for identifying structural differences. Some methodological issues related to comparative factor analysis. , 1978, Journal of Gerontology.

[12]  W. Cunningham.  Age Comparative Factor Analysis of Ability Variables in Adulthood and Old Age. , 1980 .

[13]  Jae-On Kim,et al.  Factor Analysis: Statistical Methods and Practical Issues , 1978 .

[14]  S. Maxwell,et al.  Analyzing and Interpreting Significant MANOVAs , 1982 .

[15]  C. Werts,et al.  The Use Of Analysis Of Covariance Structures For Comparing The Psychometric Properties Of Multiple Variables Across Populations. , 1978, Multivariate behavioral research.

[16]  James E. Birren,et al.  Age Changes in the Factor Structure of Intellectual Abilities in Adulthood and Old Age , 1980 .

[17]  Donald A. Rock,et al.  Comparison of correlations, variances, covariances, and regression weights with or without measurement error. , 1976 .

[18]  David A. Kenny.  Correlation and causality / David A. Kenny , 1979 .

[19]  E. M. Cramer.  Significance Tests and Tests of Models in Multiple Regression , 1972 .

[20]  Neal Schmitt,et al.  Path Analysis of Multitrait-Multimethod Matrices , 1978 .

[21]  K. Jöreskog,et al.  Analysis of linear structural relationships by maximum likelihood and least squares methods , 1983 .

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

[23]  D T Campbell,et al.  Methods Factors In Multitrait-Multimethod Matrices : Multiplicative Rather Than Additive? , 1967, Multivariate behavioral research.

[24]  J. S. Long,et al.  Estimation and Hypothesis Testing in Linear Models Containing Measurement Error , 1976 .

[25]  L. Tucker,et al.  A reliability coefficient for maximum likelihood factor analysis , 1973 .

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

[27]  K. Jöreskog.  Simultaneous factor analysis in several populations , 1971 .

[28]  P. Bentler,et al.  Significance Tests and Goodness of Fit in the Analysis of Covariance Structures , 1980 .