Aisouda Hoshiyar | Searcharxiv

arXiv2024

Regularization and Model Selection for Ordinal-on-Ordinal Regression with Applications to Food Products' Testing and Survey Data

Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done concerning ordinal-on-ordinal regression. Motivated by a consumer test and a survey on the willingness to pay for luxury food products consisting of Likert-type items, we propose a strategy for smoothing and selecting ordinally scaled predictors in the cumulative logit model. First, the group lasso is modified by the use of difference penalties on neighboring dummy coefficients, thus taking into account the predictors' ordinal structure. Second, a fused lasso-type penalty is presented for the fusion of predictor categories and factor selection. The performance of both approaches is evaluated in simulation studies and on real-world data.

stat.ME↗

arXiv2023

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

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.

stat.AP↗