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  5. Regularization and Model Selection for Item-on-Items Regression with Applications to Food Products' Survey Data
 
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Regularization and Model Selection for Item-on-Items Regression with Applications to Food Products' Survey Data

Publication date
2023-09-28
Document type
Preprint
Author
Hoshiyar, Aisouda 
Gertheiss, Laura H.
Gertheiss, Jan 
Organisational unit
Statistik und Datenwissenschaften 
DOI
10.48550/arXiv.2309.16373
URI
https://openhsu.ub.hsu-hh.de/handle/10.24405/15194
Part of the university bibliography
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Keyword
Group Lasso
Cumulative Logit
Likert-Scale
Luxury Food
Proportional Odds Model
Sensometrics
Abstract
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 survey datasets on food products consisting of Likert-type items, we propose a strategy for smoothing and selection of ordinally scaled predictors in the cumulative logit model. First, the original group lasso is modified by use of difference penalties on neighbouring dummy coefficients, thus taking into account the predictors' ordinal structure. Second, a fused lasso type penalty is presented for fusion of predictor categories and factor selection. The performance of both approaches is evaluated in simulation studies, while our primary case study is a survey on the willingness to pay for luxury food products.
Description
Grant GE2353/2-1, Deutsche Forschungsgemeinschaft (DFG)
Version
Not applicable (or unknown)
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