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Selection of influential variables in ordinal data with preponderance of zeros

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  • Ujjwal Das
  • Kalyan Das

Abstract

Presence of excess zero in ordinal data is pervasive in areas like medical and social sciences. Unfortunately, analysis of such kind of data has so far hardly been looked into, perhaps for the reason that the underlying model that fits such data, is not a generalized linear model. Obviously some methodological developments and intensive computations are required. The current investigation is concerned with the selection of variables in such models. In many occasions where the number of predictors is quite large and some of them are not useful, the maximum likelihood approach is not the automatic choice. As, apart from the messy calculations involved, this approach fails to provide efficient estimates of the underlying parameters. The proposed penalized approach includes ℓ1 penalty (LASSO) and the mixture of ℓ1 and ℓ2 penalties (elastic net). We propose a coordinate descent algorithm to fit a wide class of ordinal regression models and select useful variables appearing in both the ordinal regression and the logistic regression based mixing component. A rigorous discussion on the selection of predictors has been made through a simulation study. The proposed method is illustrated by analyzing the severity of driver injury from Michigan upper peninsula road accidents.

Suggested Citation

  • Ujjwal Das & Kalyan Das, 2021. "Selection of influential variables in ordinal data with preponderance of zeros," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 66-87, February.
    • Handle: RePEc:bla:stanee:v:75:y:2021:i:1:p:66-87
    DOI: 10.1111/stan.12225
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    References listed on IDEAS

    as
    1. Das, Ujjwal & Das, Kalyan, 2018. "Inference on zero inflated ordinal models with semiparametric link," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 104-115.
    2. Martijn Burger & Frank van Oort & Gert-Jan Linders, 2009. "On the Specification of the Gravity Model of Trade: Zeros, Excess Zeros and Zero-inflated Estimation," Spatial Economic Analysis, Taylor & Francis Journals, vol. 4(2), pages 167-190.
    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    4. Mei‐ling Sheu & Teh‐wei Hu & Theodore E. Keeler & Michael Ong & Hai‐Yen Sung, 2004. "The effect of a major cigarette price change on smoking behavior in california: a zero‐inflated negative binomial model," Health Economics, John Wiley & Sons, Ltd., vol. 13(8), pages 781-791, August.
    5. Harris, Mark N. & Zhao, Xueyan, 2007. "A zero-inflated ordered probit model, with an application to modelling tobacco consumption," Journal of Econometrics, Elsevier, vol. 141(2), pages 1073-1099, December.
    6. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    7. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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