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By Rob J. Hyndman, David M. Bashtannyk and Gary K. Grunwald

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1984). The essential process in a family of measurement models. Psychometrika 49, 529–544. D. (1990). Designing Experiments and Analyzing Data: A model Comparison Perspective. Wadsworth, Belmont, CA. Meredith, W. (1964). Notes on factorial invariance. Psychometrika 29, 177–185. , Tisak, J. (1990). Latent curve analysis. Psychometrika 55, 107–122. Messick, S. (1980). Test validity and the ethics of assessment. American Psychologist 35, 1012–1027. J. (2003). Prediction and classification in nonlinear data analysis: Something old, something new, something borrowed, something blue.

In addition, by borrowing the strategy employed by Bock and Bargmann (1966) that placed fixed values in model matrices originally intended to hold estimated parameters, SEM software may be used to fit other models as well. Meredith and Tisak (1990) described the use of the SEM model to fit latent growth models, in which the covariance structure among repeated measurements is analyzed to yield an estimate of the functional form of the unobserved (error-free) growth process. ) A similar use of the same strategy permits SEM software to be used to fit variance component models (Jöreskog and Sörbom, 1989).

Estimation of θj in the model considered so far (with the analysis conditional on θ ) is likewise straightforward: θˆj = y¯·j , (4) the mean item score for person j , using the restriction that β¯· = 0. It should be noted that this estimate is not “item free,” in the sense that it depends on the particular set of items responded to (and to which the restriction on the item parameters applies). It should also be noted that this point applies to the Rasch model as well. Now suppose person N + 1 is administered a subset S of the original n items, producing responses yi,N+1 , for i ∈ S.

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