Robust estimation in structural equation models using Bregman divergences


  • Spiridon Penev University of New South Wales
  • Tania Prvan Macquarie University



Total Bregman Distance, Structural Equation /model


Structural equation models seek to find causal relationships between latent variables by analysing the mean and the covariance matrix of some observable indicators of the latent variables. Under a multivariate normality assumption on the distribution of the latent variables and of the errors, maximum likelihood estimators are asymptotically efficient. The estimators are significantly influenced by violation of the normality assumption and hence there is a need to robustify the inference procedures. We propose to minimise the Bregman divergence or its variant, the total Bregman divergence, between a robust estimator of the covariance matrix and the model covariance matrix, with respect to the parameters of interest. Our approach to robustification is different from the standard approaches in that we propose to achieve the robustification on two levels: firstly, choosing a robust estimator of the covariance matrix; and secondly, using a robust divergence measure between the model covariance matrix and its robust estimator. We focus on the (total) von Neumann divergence, a particular Bregman divergence, to estimate the parameters of the structural equation model. Our approach is tested in a simulation study and shows significant advantages in estimating the model parameters in contaminated data sets and seems to perform better than other well known robust inference approaches in structural equation models. References
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Author Biographies

Spiridon Penev, University of New South Wales

School of Mathematics and Statistics, Associate Professor

Tania Prvan, Macquarie University

Department of Statistics, Senior Lecturer





Proceedings Computational Techniques and Applications Conference