Augmented-data projection: Internals

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 $C$ (possibly latent) response categories. For ordered response categories, the $C$ (possibly 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 $C$ stored in an attribute called ndiscrete. 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.