o2m: Perform O2PLS data integration with two-way orthogonal...
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 SCALE THE MATRICES! Any normalization you will have to do yourself. It is best practice to at least center the variables though.

o2m(
  X,
  Y,
  n,
  nx,
  ny,
  stripped = FALSE,
  p_thresh = 3000,
  q_thresh = p_thresh,
  tol = 1e-10,
  max_iterations = 1000,
  sparse = F,
  groupx = NULL,
  groupy = NULL,
  keepx = NULL,
  keepy = NULL,
  max_iterations_sparsity = 1000
)

`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)?
`p_thresh`	Integer. If `X` has more than `p_thresh` columns, a power method optimization is used, see `o2m2`
`q_thresh`	Integer. If `Y` has more than `q_thresh` columns, a power method optimization is used, see `o2m2`
`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.
`sparse`	Boolean. Default value is `FALSE`, in which case O2PLS will be fitted. Set to `TRUE` for GO2PLS.
`groupx`	Vector. Used when `sparse = TRUE`. A vector of strings indicating group names of each X-variable. Its length must be equal to the number of variables in X. The order of group names must corresponds to the order of the variables.
`groupy`	Vector. Used when `sparse = TRUE`. A vector of strings indicating group names of each Y-variable. The length must be equal to the number of variables in Y. The order of group names must corresponds to the order of the variables.
`keepx`	Vector. Used when `sparse = TRUE`. A vector of length `n` indicating how many variables (or groups if `groupx` is provided) to keep in each of the joint component of X. If the input is an integer, all the components will have the same amount of variables or groups retained.
`keepy`	Vector. Used when `sparse = TRUE`. A vector of length `n` indicating how many variables (or groups if `groupx` is provided) to keep in each of the joint component of Y. If the input is an integer, all the components will have the same amount of variables or groups retained.
`max_iterations_sparsity`	Integer. Used when `sparse = TRUE`. Maximum number of iterations for the NIPALS method for GO2PLS.

If both nx and ny are zero, o2m is equivalent to PLS2 with orthonormal loadings. This is a ‘slower’ (in terms of memory) implementation of O2PLS, and is using svd, use stripped=T for a stripped version with less output. If either ncol(X) > p_thresh or ncol(Y) > q_thresh, the NIPALS method is used which does not store the entire covariance matrix. The squared error between iterands in the NIPALS approach can be adjusted with tol. The maximum number of iterations in the NIPALS approach is tuned by max_iterations.

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
`W_gr`	Joint loadings of X at group level (only available when GO2PLS is used)
`C_gr`	Joint loadings of Y at group level (only available when GO2PLS is used)

summary.o2m, plot.o2m, crossval_o2m_adjR2, crossval_sparsity

test_X <- scale(matrix(rnorm(100*10),100,10))
test_Y <- scale(matrix(rnorm(100*11),100,11))
#  --------- Default run ------------ 
o2m(test_X, test_Y, 3, 2, 1)
#  ---------- Stripped version ------------- 
o2m(test_X, test_Y, 3, 2, 1, stripped = TRUE)
#  ---------- High dimensional version ---------- 
o2m(test_X, test_Y, 3, 2, 1, p_thresh = 1)
#  ------ High D and stripped version --------- 
o2m(test_X, test_Y, 3, 2, 1, stripped = TRUE, p_thresh = 1)
#  ------ Now with more iterations -------- 
o2m(test_X, test_Y, 3, 2, 1, stripped = TRUE, p_thresh = 1, max_iterations = 1e6)
#  ----------------------------------