Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models

Ankur Ankan, Inge Wortel, Kenneth Bollen, Johannes Textor
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:7252-7264, 2023.

Abstract

Measurement error is ubiquitous in many variables “latent-to-observed” (L2O) transformation from the MIIV approach and develop an equivalent graphical L2O transformation that allows applying existing graphical criteria to latent parameters in SEMs. We combine L2O transformation with graphical instrumental variable criteria to obtain an efficient algorithm for non-iterative parameter identification in SEMs with latent variables. We prove that this graphical L2O transformation with the instrumental set criterion is equivalent to the state-of-the-art MIIV approach for SEMs, and show that it can lead to novel identification strategies when combined with other graphical criteria.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-ankan23a, title = {Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models}, author = {Ankan, Ankur and Wortel, Inge and Bollen, Kenneth and Textor, Johannes}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {7252--7264}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/ankan23a/ankan23a.pdf}, url = {https://proceedings.mlr.press/v206/ankan23a.html}, abstract = {Measurement error is ubiquitous in many variables “latent-to-observed” (L2O) transformation from the MIIV approach and develop an equivalent graphical L2O transformation that allows applying existing graphical criteria to latent parameters in SEMs. We combine L2O transformation with graphical instrumental variable criteria to obtain an efficient algorithm for non-iterative parameter identification in SEMs with latent variables. We prove that this graphical L2O transformation with the instrumental set criterion is equivalent to the state-of-the-art MIIV approach for SEMs, and show that it can lead to novel identification strategies when combined with other graphical criteria.} }
Endnote
%0 Conference Paper %T Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models %A Ankur Ankan %A Inge Wortel %A Kenneth Bollen %A Johannes Textor %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-ankan23a %I PMLR %P 7252--7264 %U https://proceedings.mlr.press/v206/ankan23a.html %V 206 %X Measurement error is ubiquitous in many variables “latent-to-observed” (L2O) transformation from the MIIV approach and develop an equivalent graphical L2O transformation that allows applying existing graphical criteria to latent parameters in SEMs. We combine L2O transformation with graphical instrumental variable criteria to obtain an efficient algorithm for non-iterative parameter identification in SEMs with latent variables. We prove that this graphical L2O transformation with the instrumental set criterion is equivalent to the state-of-the-art MIIV approach for SEMs, and show that it can lead to novel identification strategies when combined with other graphical criteria.
APA
Ankan, A., Wortel, I., Bollen, K. & Textor, J.. (2023). Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:7252-7264 Available from https://proceedings.mlr.press/v206/ankan23a.html.

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