Loadings for Principal Component Analysis and Partial Least Squares

Computing statistical hypothesis testing for loading in principal component analysis (PCA) (Yamamoto, H. et al. (2014) ), orthogonal smoothed PCA (OS-PCA) (Yamamoto, H. et al. (2021) ), one-sided kernel PCA (Yamamoto, H. (2023) ), partial least squares (PLS) and PLS discriminant analysis (PLS-DA) (Yamamoto, H. et al. (2009) ), PLS with rank order of groups (PLS-ROG) (Yamamoto, H. (2017) ), regularized canonical correlation analysis discriminant analysis (RCCA-DA) (Yamamoto, H. et al. (2008) ), multiset PLS and PLS-ROG (Yamamoto, H. (2022) ).

loadings

Statistical hypothesis testing of loadings in multivariate analysis.

loadings provides functions for computing loading and its statistical hypothesis testing in principal component analysis and partial least squares.

• Principal component (PC) loading can be calculated from the result of the "prcomp" function. (The "loadings" function in stats can usually be applied only to the "princomp" function.) We can also calculate the p-value by statistical hypothesis testing for PC loading [1].

• Partial Least Squares (PLS) [2] (also named as Naive PLS [3]) can be computed by "pls_svd" function in loadings package. PLS loading and p-value by statistical hypothesis testing can be computed. PLS loading can also be computed from the result of the "pls_eigen" function in chemometrics.

• PLS-ROG (partial least squares rank order of groups) [3], which is a suitable PLS when the groups are ordered, can be calculated. Their loading and p-values can also be calculated.

• OS-PCA (orthogonal smoothed principal component analysis), which is a suitable PCA when the samples are ordered, can be calculated. Their loading and p-values can also be calculated.

• Multiset PLS and Multiset PLS-ROG [5] integrate multi-omics data. Their loading and p-values can also be calculated.

• One-sided kernel PCA [6], which is a partially nonlinear extension of PCA by kernel method, can be calculated. Their loading and p-values can also be calculated.

• Partial least squares discriminant analysis (PLS-DA) [7] can be calculated. Their loading and p-values can also be calculated.

• Regularized canonical correlation analysis (RCCA) [8] for discriminant analysis can be calculated. Their loading and p-values can also be calculated.

References
[1] Yamamoto H. et al., BMC Bioinformatics, (2014) 15(1):51. doi: https://doi.org/10.1186/1471-2105-15-51
[2] Barker M. et al., Journal of Chemometrics, 17(3) (2003) 166-173. doi: https://doi.org/10.1002/cem.785
[3] Yamamoto H., Journal of Chemometrics, 31(3) (2017) e2883. doi: https://doi.org/10.1002/cem.2883
[4] Yamamoto H. et al., Metabolites, 11(3) (2021) 149. doi: https://doi.org/10.3390/metabo11030149
[5] Yamamoto H., bioRxiv (2022). doi: https://doi.org/10.1101/2022.08.30.505949
[6] Yamamoto H., Jxiv (2023). doi: https://doi.org/10.51094/jxiv.262
[7] Yamamoto H.et al., Chemom. Intell. Lab. Syst., 98 (2009). doi: https://doi.org/10.1016/j.chemolab.2009.05.006
[8] Yamamoto, H. et al., Biochem. Eng. Journal, 40 (2008) 199-204. doi: https://doi.org/10.1016/j.bej.2007.12.009

Installation

The latest stable version can be installed from CRAN:

install.packages("loadings")

The latest development version can be installed from GitHub:

# install.packages("devtools")
devtools::install_github("hiroyukiyamamoto/loadings")