In this paper we focus on a multi-item Latent Growth Curve (LGC) model for modelling change across time of a latent variable measured by multiple items at different occasions: in the structural part the latent variable grows according to a random slope linear model, whereas in the measurement part the latent variable is measured at each occasion by a conventional factor model with time-invariant loadings. The specification of a multi-item LGC model involves several interrelated choices: indeed, the features of the structural part, such as the functional form of the growth, are linked to the features of the measurement part, such as the correlation structure across time of measurement errors. In the paper, we give guidelines on the specification of the variance-covariance structure of measurement errors. In particular, we investigate the empirical implications of different specification strategies through an analysis of student ratings collected in four academic years about courses of the University of Florence. In the application we compare the compound symmetry correlation structure with the independence structure. In particular, we discuss the implications of the two specifications in terms of interpretability of the results.
Specification issues in latent growth models with multiple indicators / L. Grilli; R. Varriale. - STAMPA. - 10:(2011), pp. 1-9. (Intervento presentato al convegno SIS 2011 Statistical Conference tenutosi a Bologna nel June 8, 2011- June 10, 2011).
Specification issues in latent growth models with multiple indicators
GRILLI, LEONARDO;
2011
Abstract
In this paper we focus on a multi-item Latent Growth Curve (LGC) model for modelling change across time of a latent variable measured by multiple items at different occasions: in the structural part the latent variable grows according to a random slope linear model, whereas in the measurement part the latent variable is measured at each occasion by a conventional factor model with time-invariant loadings. The specification of a multi-item LGC model involves several interrelated choices: indeed, the features of the structural part, such as the functional form of the growth, are linked to the features of the measurement part, such as the correlation structure across time of measurement errors. In the paper, we give guidelines on the specification of the variance-covariance structure of measurement errors. In particular, we investigate the empirical implications of different specification strategies through an analysis of student ratings collected in four academic years about courses of the University of Florence. In the application we compare the compound symmetry correlation structure with the independence structure. In particular, we discuss the implications of the two specifications in terms of interpretability of the results.File | Dimensione | Formato | |
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