# st: Interactions & Long's PRCHANGE (pred probs from LDVs)

 From "John Reynolds" To Subject st: Interactions & Long's PRCHANGE (pred probs from LDVs) Date Tue, 9 Mar 2004 11:52:08 -0500

```Looking for help w/ Long & Freese's PRCHANGE, part of their SPOST collection
of ado files to help interpret limited dependent variable models.

Question:
How can I generate accurate predicted probabilities w/ PRCHANGE if my
covariate of interest is "involved" in an interaction term?

Details:
I'm estimating ordered probit models that include an interaction term
between a dummy variable and interval variable.  For simplicitly, assume the
following model, Y = b0 + b1*dummy + b2*interval + b3*dummy*interval.  Long
& Freese's PRCHANGE generates predicted probabilities and changes in
probability holding all other variables constant at their sample means or at
a pre-specified value.  I want predicted probabilities for the two groups
represented by the dummy variable, holding the interval variable constant at
its sample mean.
E.g.,
oprobit y dummy intval intxn
prchange, x(dummy=1)
would generate the predicted probabilities that y = k for cases which equal
1 on the dummy variable, holding the interval variable and the interaction
term constant at their sample means.  The problem is that the sample mean of
"intval" would be the mean of the interval for all cases in the sample,
while the sample mean of the interaction term "intxn" would equal the sum of
the interval variable for dummy = 1 only, divided by the sample size.
Instead, if I were to calculate the predicted probabilities by hand, I would
use 1*(sample mean of interval variable) corresponding to dummy*interval.
The issue is equally problematic when turning to the reference group on the
dummy variable, i.e.,
oprobit y dummy intval intxn
prchange, x(dummy=0).
This model would estimate predicted probabilities and would again include a
contribution of the interaction, even though the interaction term should
drop out since it equals 0 for all dummy=0.

Summary:
Should I specify that PRCHANGE use group-specific means for the interaction
terms, and overal sample means for the rest?  Can I specify that with
PRCHANGE?  Is there a simpler solution I'm overlooking?  For those of you
how have a copy of Long & Freese's Stata book, could you verify for me
whether this is addressed in section "8.2.1 Computing gender differences in
predictions with interactions?"  I plan to use this book next fall for
class, but haven't bought it yet.

Thanks for any assistance.

John Reynolds, PhD
Department of Sociology
Florida State University
Tallahassee, FL 32306-2270
850-644-4321
850-644-2304 (fax)
email: john.reynolds@fsu.edu

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