Re: Deriving Formula from Ordinal Regression Results to Classify New Cases?

Posted by Ryan on
URL: http://spssx-discussion.165.s1.nabble.com/Deriving-Formula-from-Ordinal-Regression-Results-to-Classify-New-Cases-tp5715848p5715990.html

Vik,

I found an example fitting an ordinal logistic regression model using
the PLUM procedure here:

http://www.ats.ucla.edu/stat/SPSS/dae/ologit.htm

The SPSS dataset used for that example is located here:

http://www.ats.ucla.edu/stat/data/ologit.sav

The dependent variable "apply" has three ordered categories (0, 1, and 2).
The independent variables are "pared", "public", and "gpa".

The syntax to fit the model AND obtain the estimated probability of
each category for each subject is:

plum apply with pared public gpa
 /link = logit
 /print = parameter summary
 /save=estprob.

Let's apply the equations I provided previously to the data from the
FIRST subject using COMPUTE:

compute #eta0_subj1 = 2.203323 - (1.047664*0 + (-0.058683)*0 +
0.615746*3.260000).
compute #eta1_subj1 = 4.298767 - (1.047664*0 + (-0.058683)*0 +
0.615746*3.260000).

compute #cum_prob_0_subj1 = 1 / (1 + exp(-#eta0_subj1)).
compute #cum_prob_0_1_subj1 = 1 / (1 + exp(-#eta1_subj1)).
compute #cum_prob_0_1_2_subj1 = 1.

compute prob_0_subj1 = #cum_prob_0_subj1.
compute prob_1_subj1 = #cum_prob_0_1_subj1 - #cum_prob_0_subj1.
compute prob_2_subj1 = #cum_prob_0_1_2_subj1 - #cum_prob_0_1_subj1.
execute.

As you can see, the predicted probabilities for subject 1
(prob0_subj1, prob1_subj1, prob2_subj1) match exactly those produced
by the SAVE subcommand of the PLUM procedure.

Just to make sure there is no misundertanding, 2.203323 and 4.298767
are the threshold parameter estimates. 1.047664, -0.058683, and
0.615746 are the location parameter estimates. 0, 0, and 3.260000 are
the independent variable values (pared, public, and gpa, respectively)
for subject 1.

Finally, since the probability of category 0 is the highest for
subject 1 (prob_0_subj1 =.548842), it [category 0] is the predicted
category for subject 1.

Ryan

On Wed, Oct 31, 2012 at 1:15 PM, Vik Rubenfeld <[hidden email]> wrote:

>
> Very good. Thanks.
>
>
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