The LASSO on latent indices for regression modeling with ordinal categorical predictors

Francis K.C. Hui, Samuel Müller and A.H. Welsh

Computational Statistics & Data Analysis, 2020, vol. 149, issue C

Abstract: Many applications of regression models involve ordinal categorical predictors. Two common approaches for handling ordinal predictors are to form a set of dummy variables, or employ a two stage approach where dimension reduction is first applied and then the response is regressed against the predicted latent indices. Both approaches have drawbacks, with the former running into a high-dimensional problem especially if interactions are considered, while the latter separates the prediction of the latent indices from the construction of the regression model. To overcome these challenges, a new approach called the LASSO on Latent Indices (LoLI) for handling ordinal predictors in regression is proposed, which involves jointly constructing latent indices for each or for groups of ordinal predictors and modeling the response directly as a function of these. LoLI borrows strength from the response to more accurately predict the latent indices, leading to better estimation of the corresponding effects. Furthermore, LoLI incorporates a LASSO type penalty to perform hierarchical selection, with interaction terms selected only if both parent main effects are included. Simulations show that LoLI can outperform the dummy variable and two stage approaches in selection and prediction performance. Applying LoLI to an Australian household-based panel identified three dimensions of psychosocial workplace quality (job demands, stress, and security) which affect an individual’s mental health in an additive and pairwise interactive manner.

Keywords: Dimension reduction; Factor analysis; Factor variables; Interaction; Latent variables; Model selection (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947320300426
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:149:y:2020:i:c:s0167947320300426

DOI: 10.1016/j.csda.2020.106951

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().