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For regression with ordered response variable, there are different methods, for example, discriminant analysis, probit or logit model. I am wondering what are the different focuses of the different methods and which one is more often used.

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    $\begingroup$ It's almost axiomatic that statistical people don't have good data on anything like uses of statistical methods, statistical software, etc. But you could search your favourite citation database to get some indications. But relative use doesn't tell you much about desirability, at least not much more than newspaper circulation or book sales figures tell you what's worth reading. $\endgroup$
    – Nick Cox
    Oct 14, 2013 at 16:03

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I don't think that discriminant analysis will be very efficient because it does not use the ordering. There are 4 commonly used families for ordinal response that are based on direct probability modeling: logistic, probit, log-log (Cox model) and complementary log-log. These are implemented in the R rms package orm function, which also handles continuous $Y$. Graphical methods can be used to choose from among the 4. Proportional odds is the easiest to interpret.

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  • $\begingroup$ Thanks so much. Can you please give a reference to the graphical methods used to choose among the 4 models? $\endgroup$
    – user13154
    Oct 14, 2013 at 15:29
  • $\begingroup$ Stratify by a top predictor and within each stratum compute the inverse transformation (logit, etc.) of the cumulative proportion $Y \geq y$ for all $y$ above $min(Y)$. Look for parallelism. $\endgroup$ Oct 14, 2013 at 15:55

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