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The true-change model with individual method
effects: Reliability issues
Ste ´phane Vautier
1
*, Rolf Steyer
2
and Anne Boomsma
3
1
Centre d’e ´tude et de recherche en psychopathologie, Universite ´ de Toulouse,
France
2
Institut fu ¨r Psychologie, Friedrich Schiller University, Jena, Germany
3
Department of Sociology, Faculty of Behavioural and Social Sciences, University of
Groningen, The Netherlands
The true intra-individual change model is generalized by defining individual method
effects. This allows the analysis of non-congeneric test–retest variables assumed to
measure a common, possibly (temporally) transient, attribute. Temporal change in the
attribute between different times of measurement is modelled by the true-change
variable. Individual causal method effects, due to heterogeneity of the measurement
methods, account for the imperfect correlation of the true-score variables at each time
of measurement. The reliability of the composite scores, at each time of measurement,
and the reliability of the difference composite score may be estimated with appropriate
coefficients derived from the model. Measurements of daily life tension in adult females
serve to illustrate how the model can be used empirically.
1. Introduction
Estimation of the reliability of a sum of manifest variables is a long-running
methodological research issue in the social and behavioural sciences (e.g. Feldt &
Brennan, 1989; Li, Rosenthal, & Rubin, 1996; McDonald, 1999; Raykov, 2001b, 2001c;
Stanley, 1971; Steyer & Schmitt, 1990a; Thorndike, 1951; Weiss & Davison, 1981;
Zimmerman & Williams, 1998; Zumbo & Rupp, 2004). The congeneric model (Jo ¨reskog,
1971), which subsumes other classical and more restrictive models, inspired a series of
papers focused on the estimation of the reliability of a sum of congeneric variables (e.g.
Kano & Azuma, 2003; Raykov, 1997a, 1998, 2001b; Reuterberg & Gustafsson, 1992).
(Measurement variables are congeneric if (a) the corresponding true-score variables are
linearly and positively related and (b) the measurement error variables are uncorrelated
* Correspondence should be addressed to Ste ´phane Vautier, Centre d’e ´tudes et de recherche en psychopathologie, Maison de
la Recherche, 5 alle ´es A. Machado, 31058 Toulouse Cedex 9, France (e-mail: vautier@univ-tlse2.fr).
The
British
Psychological
Society
379
British Journal of Mathematical and Statistical Psychology (2008), 61, 379–399
q 2008 The British Psychological Society
www.bpsjournals.co.uk
DOI:10.1348/000711007X206826