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Computation of the covariance matrix implied by a recursive structural equation model with latent variables

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Abstract

Structural Equation Modelling is a multivariate technique that allows us to analyze causal relationships between hypothetical constructs, each measured by several observable variables. The computation of the covariance matrix implied by the model is a crucial step in the whole modelling process. In this paper, a new theorem for the computation of the implied covariance matrix is proposed. This theorem will be useful to find the classical Jöreskog’s formula. Besides, it will be the basis for introducing a new method for computation based on the Finite Iterative Method. Finally, theoretical and computational comparisons between the proposed method and Jöreskog’s formula are also discussed and illustrated.

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Acknowledgements

The present paper is an extension of a conference proceeding that can be accessed at https://ieeexplore.ieee.org/document/8727648/. This extension contains advanced theoretical as well as numerical results.

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Authors and Affiliations

  1. Center of Mathematical Researches and Applications, Faculty of Sciences, Mohammed V University in Rabat, Rabat, Morocco

    Zouhair El Hadri

  2. C3S Laboratory, Hassan II University of Casablanca, Casablanca, Morocco

    M’barek Iaousse

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  1. Zouhair El Hadri
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  2. M’barek Iaousse
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Correspondence to M’barek Iaousse.

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Hadri, Z.E., Iaousse, M. Computation of the covariance matrix implied by a recursive structural equation model with latent variables. Qual Quant 56, 4295–4311 (2022). https://doi.org/10.1007/s11135-022-01321-z

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