The augmented-data projection makes extensive use of augmented-rows
matrices and augmented-length vectors. In the following, \(N\),
\(C_{\mathrm{cat}}\), \(C_{\mathrm{lat}}\),
\(S_{\mathrm{ref}}\), and \(S_{\mathrm{prj}}\) from help
topic refmodel-init-get are used. Furthermore, let \(C\) denote either
\(C_{\mathrm{cat}}\) or \(C_{\mathrm{lat}}\), whichever is
appropriate in the context where it is used (e.g., for ref_predfun's
output, \(C = C_{\mathrm{lat}}\)). Similarly, let \(S\) denote
either \(S_{\mathrm{ref}}\) or \(S_{\mathrm{prj}}\),
whichever is appropriate in the context where it is used. Then an
augmented-rows matrix is a matrix with \(N \cdot C\) rows in \(C\)
blocks of \(N\) rows, i.e., with the \(N\) observations nested in the
\(C\) (latent) response categories. For ordered response categories, the
\(C\) (latent) response categories (i.e., the row blocks) have to be sorted
increasingly. The columns of an augmented-rows matrix have to correspond to
the \(S\) parameter draws, just like for the traditional projection. An
augmented-rows matrix is of class augmat (inheriting from classes matrix
and array) and needs to have the value of \(N\) stored in an attribute
called nobs_orig. An augmented-length vector (class augvec) is the vector
resulting from subsetting an augmented-rows matrix to extract a single column
and thereby dropping dimensions.