Abstract
OnPLS was recently proposed as a general extension of O2PLS for applications in multiblock and path model analysis. OnPLS is very similar to O2PLS in the case with two matrices, but generalizes symmetrically to cases with more than two matrices without giving preference to any matrix.
OnPLS extracts a minimal number of globally joint components that exhibit maximal covariance and correlation. A number of locally joint components are also extracted. These are shared between some matrices, but not between all. These components are also maximally covarying with maximal correlation. The variation that remains after the joint and locally joint variation has been extracted is unique to a particular matrix. This unique variation is orthogonal to all other matrices and captures phenomena specific in its matrix.
The method’s utility has been demonstrated by its application to synthetic datasets with very good results in terms of its ability to decompose the matrices. It has been shown that OnPLS affords a reduced number of globally joint components and increased intercorrelations of scores, and that it greatly facilitates interpretation of the models. Preliminary results in the application on real data has also given positive results. The results are similar to previous results using other multiblock and path model methods, but afford an increased interpretability because of the locally joint and unique components.
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Löfstedt, T., Hanafi, M., Trygg, J. (2013). Multiblock and Path Modeling with OnPLS. In: Abdi, H., Chin, W., Esposito Vinzi, V., Russolillo, G., Trinchera, L. (eds) New Perspectives in Partial Least Squares and Related Methods. Springer Proceedings in Mathematics & Statistics, vol 56. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8283-3_14
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