Penalized Optimal Scaling for Ordinal Variables with an Application to International Classification of Functioning Core Sets

TL;DR

This paper introduces a penalized optimal scaling method for ordinal variables in PCA, improving interpretability and predictive performance, demonstrated through an application to the ICF classification system.

Contribution

It proposes a novel penalized non-linear PCA approach for ordinal data, bridging standard PCA and non-linear PCA, with enhanced interpretability and validation performance.

Findings

Better interpretability of non-linear transformations

Improved validation performance over existing methods

Effective application to ICF ordinal data

Abstract

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric implying linear relationships between the variables at hand, or non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels as well as better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.