This function implements the Net Analyte Signal (NAS) algorithm, as proposed by Lorber (1997), which involves the concentration matrix. NAS aims to remove information from the predictor variables, that is orthogonal or irrelevant to the response variable(s) by orthogonal projection.
Arguments
- x
A matrix or data frame of the predictor variables
- y
A vector, matrix or data frame of the response variable(s)
- ncomp
An integer specifying the number of principal components to retain for orthogonal processing. Default is 5.
- center
A logical value specifying whether to center the data. Default is
TRUE.- scale
A logical value specifying whether to scale the data. Default is
FALSE.
Details
The NAS algorithm aims to obtain a corrected matrix that contains only the information relevant to the response variable \(\textbf{Y}\). This is achieved by constructing an orthogonal projection matrix based on the principal components of the data matrix, \(\textbf{X}\), that are orthogonal to \(\textbf{Y}\). The corrected matrix is then obtained by projecting \(\textbf{X}\) onto the subspace orthogonal to the unwanted components.