Class ExplicitImplicitModelPCA

  • Direct Known Subclasses:
    AverageImplicitModelPCA

    public class ExplicitImplicitModelPCA
    extends Object
    Given a time series of vectored observations, we decompose them into a reduced dimension of linear sum of both explicit/specified and implicit factors. The implicit factors are orthogonal. The user specifies the time series of observations and th explicit factor values over time. Specifically, we have \(R = Γ'G + \bar{R} + {B}'F + E\) R is the time series of vectored observation. Its size is N x T. G is the time series of the explicit factor values. Its size is M x T, where M is the number of implicit factors. Γ' is the matrix of factor loadings for explicit factors. Its size is N x M. Each row is the explicit factor loadings for each subject. R_bar is the average of each subject's value over time, one entry per subject. It size is N. We copy the vector T times by columns to form a matrix for computation. F is the time series of the implicit factor values. Its size is K x T, where K is the number of implicit factors. B' is the matrix of implicit factor loadings. Its size is N x K. Each row is the implicit factor loadings for each subject. E is the residual matrix.