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Ordered-Categorical Data
We are in an even better position to guess at Person 1’s score on the numeric
variable that underlies item1 because Person 1 gave a response to item1. This person’s
response places his or her score in the middle interval, between the two boundaries.
Since the two boundaries were arbitrarily fixed at 0 and 1, we know that the score is
somewhere between 0 and 1, but it seems like we should be able to say more than that
by using the person’s responses on the other variables along with the assumption that
the model is correct.
In Bayesian estimation, all unknown quantities are treated in the same way. Just as
unknown parameter values are estimated by giving their posterior distribution, so are
unknown data values. A posterior distribution for an unknown data value is called a
posterior predictive distribution, but it is interpreted just like any posterior
distribution. To view posterior predictive distributions for unknown data values:
E Click the Posterior Predictive button .
or
E From the menus, choose View > Posterior Predictive.
The Posterior Predictive Distributions window appears.