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Zahid, Faisal Maqbool and Heumann, Christian (2011): Regularized Proportional Odds Models. Department of Statistics: Technical Reports, No.103
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Abstract

The proportional odds model is commonly used in regression analysis to predict the outcome for an ordinal response variable. The maximum likelihood approach becomes unstable or even fails in small samples with relatively large number of predictors. The ML estimates also do not exist with complete separation in the data. An estimation method is developed to address these problems with MLE. The proposed method uses pseudo observations to regularize the observed responses by sharpening them so that they become close to the underlying probabilities. The estimates can be computed easily with all commonly used statistical packages supporting the fitting of proportional odds models with weights. Estimates are compared with MLE in a simulation study and two real life data sets.