The Manifest Association Structure of Structural Equation Models for Longitudinal Data: Insights from Partial Correlations
Peter W.F. Smith1, Maria de Fátima Salgueiro2
1Southampton Statistical Sciences Research Institute, University of Southampton, Hampshire, United Kingdom; 2ISCTE-IUL and UNIDE, Lisbon University Institute, Lisbon, Portugal

Salgueiro, Smith and McDonald (2008, Psychometrika) investigated the association structure between manifest variables arising from the single-factor model using partial correlations and demonstrated how extra insight into these models can be obtained by using a partial correlations parameterization. Salgueiro, Smith and McDonald (2010, Journal of Multivariate Behavioral Research) investigated the connections between graphical Gaussian models and classical single-factor models by parameterizing the single-factor model as a graphical Gaussian model. The associations between each manifest variable and the latent factor were measured by factor partial correlations and the manifest partial correlations were expressed as a function of the factor partial correlations.

In this paper we extend these investigations to structural equation models for longitudinal data. Here we derive the manifest partial correlations of a three-wave single-indicator measurement model, a two-wave, two-indicator measurement model and a two-wave, three-indicator model with and without correlated measurement errors. We also parameterize these models using factor partial correlations to specify the dependence of the latent variables on the manifest variables. The results are illustrated using examples taken from Finkel (1995, Causal Analysis with Panel Data), including one concerning attitudinal change during the 1980 presidential campaign as measured by the American National Election Study. We assess the extra insight gained by inspection of the manifest partial correlations and using factor partial correlations to parameterize the models. Potential benefits include ruling out models on the grounds that the observed manifest partial correlations are incompatible with those imposed by the model and an alternative approach to assessing the goodness of fit of the models.

Keywords: Factor partial correlations; Panel data; Manifest partial correlations; Structural equation models

Biography: Peter Smith is Director of Southampton Statistical Sciences Research Institute and Professor of Social Statistics at the University of Southampton in the UK, where he has worked for over twenty years. He has a BSc in Mathematics from Lancaster University, an MSc in Probability and Statistics from the University of Shefield and a PhD in Statistics also from Lancaster University. His general research interests are in developing new statistical methodology and applying sophisticated statistical methods to problems in demography, medicine and health. His expertise includes the modelling of complex survey data, both cross-sectional and longitudinal.