approxloads

Uses the eigendecomposition of a square, symmetrix matrix R to obtain the
loadings matrix L such that R is approximated by LL', with L restricted to
have <code>r</code> columns. Hence LL' is a rank <code>r</code> approximation of R. The
eigendecomposition of R is used to obtain L from the first <code>r</code>
eigenvectors and eigenvalues. In case <code>procr.target</code> is not
<code>NULL</code>, L is further rotated through orthogonal Procrustes analysis to
match as closely as possible the matrix <code>procr.target</code> through
<code>orthprocr</code>.

This is an implementation of constrained dual scaling for
detecting response styles in categorical data, including utility functions. The
procedure involves adding additional columns to the data matrix representing the
boundaries between the rating categories. The resulting matrix is then doubled
and analyzed by dual scaling. One-dimensional solutions are sought which provide
optimal scores for the rating categories. These optimal scores are constrained
to follow monotone quadratic splines. Clusters are introduced within which the
response styles can vary. The type of response style present in a cluster can
be diagnosed from the optimal scores for said cluster, and this can be used to
construct an imputed version of the data set which adjusts for response styles.

Pieter Schoonees

Constrained Dual Scaling for Detecting Response Styles

approxloads function

<dl><dt>R</dt>
<dd>Square, symmetric matrix R to be approximated</dd>
<dt>r</dt>
<dd>The required rank of the approximation</dd>
<dt>procr.target</dt>
<dd>Optional; the target matrix for L in the orthogonal
Procrustes analysis</dd>
<dt>refl.target</dt>
<dd>Optional; the matrix to check against for possible
reflections of the loading vectors.</dd></dl>

Arguments

Low Rank Approximation LL' of a Square Symmetrix Matrix R — approxloads

<dl>

<dt>R</dt>
<dd>Square, symmetric matrix R to be approximated</dd>


<dt>r</dt>
<dd>The required rank of the approximation</dd>


<dt>procr.target</dt>
<dd>Optional; the target matrix for L in the orthogonal
Procrustes analysis</dd>


<dt>refl.target</dt>
<dd>Optional; the matrix to check against for possible
reflections of the loading vectors.</dd>

</dl>

approxloads: Low Rank Approximation LL' of a Square Symmetrix Matrix R

Description

Usage

Arguments

Examples