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I am working on a data set of about 34K rows trying to predict an ordinal response variable using R. I have tried association rules, random forest and ordinal regression. Does anyone have experience with other algorithms which are worth a try?

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You labeled your question as "classification" but you are not doing classification; you are doing prediction. Ordinal regression models are dedicated to this problem and you have many good choices. The most commonly used ordinal models model cumulative probabilities. These include the proportional odds model (logit link) and probit- and log-log links. All these are implemented efficiently in the R rms package orm function, which allows $Y$ to be continuous and not just discrete. A detailed case study may be found in Handouts under http://biostat.mc.vanderbilt.edu/CourseBios330.

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