Specifying Measurement Error Correlations in Latent Growth Curve Models With Multiple Indicators

In this tutorial paper we focus on a multi-item Latent Growth Curve model for modeling 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 Latent Growth Curve 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 three correlation structures (independence, lag-1, and compound symmetry), illustrating the differences in terms of substantive assumptions, model fit, and interpretability of the results.