## Determining Observations for Likelihood Contributions

Suppose the response variable can take on the ordered values
**1, ... , ***k*, *k*+1
where *k* is an integer . If you use
*events/trials* syntax,
each observation is split into two observations. One has response value 1 with
a frequency equal to the frequency of the original observation (which is 1 if
the FREQ statement is not used)
times the value of the *events* variable. The
other observation has
response value 2 and a frequency equal to the
frequency of the original observation times the value
of (*trials ***-** events). These two observations will have
the same explanatory variable values and the same FREQ and WEIGHT
values as the original observation.

For either *single-trial* or *events/trials* syntax,
let *j* index all observations.
In other words, for *single-trial* syntax, *j* indexes the
actual observations. And, for *events/trials* syntax,
*j* indexes the observations after splitting (as described previously).
If your data set has 30 observations and you use *single-trial* syntax,
*j* has values from 1 to 30; if you use *events/trials*
syntax, *j* has values from 1 to 60.

The likelihood for the *j*th observation with ordered response
value *y*_{j} and explanatory variables vector
**x**_{j} is given by

where *F*(.) is the logistic, normal, or extreme-value distribution function,
are
intercept parameters, and is the slope parameter vector.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.