Abstract
The sample space of a manifest random vector is of crucial importance for a latent variable model. Compositional data require an appropriate statistical analysis because they provide the relative importance of the parts of a whole. Any statistical model including variables created using the original parts should be formulated according to the geometry of the simplex. Methods based on log-ratio coordinates give a consistent framework for analyzing this type of data. Here, we introduce an approach that includes both the orthonormal log-ratio coordinates and an auxiliary variable carrying absolute information and illustrate it through the factor analysis of two real datasets.
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Acknowledgements
This work has been partially financed by the CODAMET project (Ministerio de Ciencia, Innovación y Universidades; Ref: RTI2018-095518-B-C21).
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Barceló-Vidal, C., Martín-Fernández, J.A. (2021). Factor Analysis of Compositional Data with a Total. In: Filzmoser, P., Hron, K., Martín-Fernández, J.A., Palarea-Albaladejo, J. (eds) Advances in Compositional Data Analysis. Springer, Cham. https://doi.org/10.1007/978-3-030-71175-7_7
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