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Ordinal ridge regression with categorical predictors
- Source :
- Journal of Applied Statistics. 39:161-171
- Publication Year :
- 2012
- Publisher :
- Informa UK Limited, 2012.
-
Abstract
- In multi-category response models, categories are often ordered. In the case of ordinal response models, the usual likelihood approach becomes unstable with ill-conditioned predictor space or when the number of parameters to be estimated is large relative to the sample size. The likelihood estimates do not exist when the number of observations is less than the number of parameters. The same problem arises if constraint on the order of intercept values is not met during the iterative procedure. Proportional odds models (POMs) are most commonly used for ordinal responses. In this paper, penalized likelihood with quadratic penalty is used to address these issues with a special focus on POMs. To avoid large differences between two parameter values corresponding to the consecutive categories of an ordinal predictor, the differences between the parameters of two adjacent categories should be penalized. The considered penalized-likelihood function penalizes the parameter estimates or differences between the para...
- Subjects :
- Statistics and Probability
Ordinal data
Logistic regression
Ordinal regression
Regression
Statistics::Computation
Constraint (information theory)
Sample size determination
Statistics
Econometrics
Statistics::Methodology
Ordered logit
Statistics, Probability and Uncertainty
Categorical variable
Mathematics
Subjects
Details
- ISSN :
- 13600532 and 02664763
- Volume :
- 39
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Statistics
- Accession number :
- edsair.doi...........b426465231e669d8cbc1d45c72926d1e