Longitudinal Con rmatory Factor Analysis for Polytomous Item Responses: Model De nition and Model Selection on the Basis of Stochastic Measurement Theory

Based on a distinction between four di erent models of longitudinal con rmatory factor analysis (LCFA) originally explained by Marsh and Grayson (1994) an analogous class of LCFA models for polytomous variables is described. Then, the probabilistic foundations of LCFA models for polytomous variables are explained and it is shown that only two models of the initially considered four LCFA models can be de ned as stochastic measurement models on the basis of an explicated random experiment. For these two models the representation, uniqueness, and meaningfulness theorems are proven and it is shown how some implications of these models can be tested. The two stochastic measurement LCFA models are illustrated by a short empirical application. Finally, the results are discussed with respect to the role of stochastic measurement theory for the de nition and selection of di erent LCFA models.

[1]  M. Eid,et al.  Measuring Variability and Change With an Item Response Model for Polytomous Variables , 1998 .

[2]  Jan de Leeuw,et al.  On the relationship between item response theory and factor analysis of discretized variables , 1987 .

[3]  R. Steyer,et al.  States and traits in psychological assessment. , 1992 .

[4]  Herbert W. Marsh,et al.  Stability of Individual Differences in Multiwave Panel Studies: Comparison of Simplex Models and One‐Factor Models , 1993 .

[5]  A. Neubauer,et al.  Situational effects in trait assessment: The FPI, NEOFFI, and EPI questionnaires , 1995 .

[6]  A Zautra,et al.  The trait-state-error model for multiwave data. , 1995, Journal of consulting and clinical psychology.

[7]  Karl G. Jöreskog,et al.  New developments in LISREL: analysis of ordinal variables using polychoric correlations and weighted least squares , 1990 .

[8]  Melvin R. Novick,et al.  Statistical Theories of Mental Test Scores , 1969 .

[9]  E. Muraki,et al.  Full-Information Item Factor Analysis , 1988 .

[10]  James E. Carlson,et al.  Full-Information Factor Analysis for Polytomous Item Responses , 1995 .

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

[12]  Patrick Suppes,et al.  Basic measurement theory , 1962 .

[13]  Donald B. Rubin,et al.  The Dependability of Behavioral Measurements: Theory of Generalizability for Scores and Profiles. , 1974 .

[14]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[15]  H. Gulliksen.  Theory of mental tests , 1952 .

[16]  Herbert W. Marsh,et al.  Longitudinal confirmatory factor analysis: Common, time‐specific, item‐specific, and residual‐error components of variance , 1994 .

[17]  M. Eid,et al.  Validating scales for the assessment of mood level and variability by latent state-trait analyses , 1994 .

[18]  C. H. Coombs,et al.  Mathematical psychology : an elementary introduction , 1970 .

[19]  M. Eid,et al.  Cortisol and behavior: 2. Application of a Latent state-trait model to salivary cortisol , 1990, Psychoneuroendocrinology.

[20]  C. Hertzog,et al.  Beyond autoregressive models: some implications of the trait-state distinction for the structural modeling of developmental change. , 1987, Child development.

[21]  Robert J. Mislevy,et al.  Recent Developments in the Factor Analysis of Categorical Variables , 1986 .

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

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