o2m2: Perform O2-PLS with two-way orthogonal corrections
In OmicsPLS: Data Integration with Two-Way Orthogonal Partial Least Squares

Description Usage Arguments Details Value See Also Examples

NOTE THAT THIS FUNCTION DOES NOT CENTER NOR SCALES THE MATRICES! Any normalization you will have to do yourself. It is best practice to at least center the variables though.

1	o2m2(X, Y, n, nx, ny, stripped = TRUE, tol = 1e-10, max_iterations = 100)

`X`	Numeric matrix. Vectors will be coerced to matrix with `as.matrix` (if this is possible)
`Y`	Numeric matrix. Vectors will be coerced to matrix with `as.matrix` (if this is possible)
`n`	Integer. Number of joint PLS components. Must be positive.
`nx`	Integer. Number of orthogonal components in X. Negative values are interpreted as 0
`ny`	Integer. Number of orthogonal components in Y. Negative values are interpreted as 0
`stripped`	Logical. Use the stripped version of o2m (usually when cross-validating)?
`tol`	Double. Threshold for which the NIPALS method is deemed converged. Must be positive.
`max_iterations`	Integer. Maximum number of iterations for the NIPALS method.

If both nx and ny are zero, o2m2 is equivalent to PLS2 with orthonormal loadings. For cross-validation purposes, consider using stripped = TRUE.

Note that in this function, a power-method based approach is used when the data dimensionality is larger than the sample size. E.g. for genomic data the covariance matrix might be too memory expensive.

A list containing

`Tt`	Joint X scores
`W.`	Joint X loadings
`U`	Joint Y scores
`C.`	Joint Y loadings
`E`	Residuals in X
`Ff`	Residuals in Y
`T_Yosc`	Orthogonal X scores
`P_Yosc.`	Orthogonal X loadings
`W_Yosc`	Orthogonal X weights
`U_Xosc`	Orthogonal Y scores
`P_Xosc.`	Orthogonal Y loadings
`C_Xosc`	Orthogonal Y weights
`B_U`	Regression coefficient in `Tt` ~ `U`
`B_T.`	Regression coefficient in `U` ~ `Tt`
`H_TU`	Residuals in `Tt` in `Tt` ~ `U`
`H_UT`	Residuals in `U` in `U` ~ `Tt`
`X_hat`	Prediction of X with Y
`Y_hat`	Prediction of Y with X
`R2X`	Variation (measured with `ssq`) of the modeled part in X (defined by joint + orthogonal variation) as proportion of variation in X
`R2Y`	Variation (measured with `ssq`) of the modeled part in Y (defined by joint + orthogonal variation) as proportion of variation in Y
`R2Xcorr`	Variation (measured with `ssq`) of the joint part in X as proportion of variation in X
`R2Ycorr`	Variation (measured with `ssq`) of the joint part in Y as proportion of variation in Y
`R2X_YO`	Variation (measured with `ssq`) of the orthogonal part in X as proportion of variation in X
`R2Y_XO`	Variation (measured with `ssq`) of the orthogonal part in Y as proportion of variation in Y
`R2Xhat`	Variation (measured with `ssq`) of the predicted X as proportion of variation in X
`R2Yhat`	Variation (measured with `ssq`) of the predicted Y as proportion of variation in Y

o2m

# This takes a couple of seconds on an intel i5
system.time(
             o2m2(matrix(rnorm(50*2000),50),matrix(rnorm(50*2000),50),1,0,0)
)

# This however takes 10 times as much...
# system.time(
#              o2m(matrix(rnorm(50*2000),50),matrix(rnorm(50*2000),50),1,0,0,
#              p_thresh = 1e4,q_thresh = 1e4)  # makes sure power method is not used
# )