[R] Predicting ordinal outcomes using lrm{Design}

jayhegde hegde at umn.edu
Tue Apr 15 20:49:26 CEST 2008

Dear List,
    I have two questions about how to do predictions using lrm, specifically
how to predict the ordinal response for each observation *individually*.  
I'm very new to cumulative odds models, so my apologies if my questions are
too basic.

    I have a dataset with 4000 observations.  Each observation consists of
an ordinal outcome y (i.e., rating of a stimulus with four possible ratings,
1 through 4), and the values of two predictor variables x1 and x2 associated
with each stimulus:

Obs#       y          x1       x2
1             3         2.35   -1.07
2             2         1.78   -0.66
3             4         5.19   -3.51
4000        1        0.63   -0.23

I get excellent fits using

  fit1 <-lrm(y ~ x1+x2, data=my.dataframe1)

Now I want to see how well my model can predict y for a new set of 4000
observations.  I need to predict y for each new observation *individually*.
I know an expression like

  predicted1<-predict(fit1, newdata=my.dataframe2, type=""fitted.ind")

can give *probability* of each of the 4 possible responses for each
observation.  So my questions are

  (1) How do I pick the likeliest y (i.e., likeliest of the 4 possible
ratings) for each given new observation?

  (2) Are there good reference that explain the theory behind this type of
prediction to a beginner like me?

   Thank you very much,
   Jay Hegdé
   Univeristy of Minnesota

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