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st: From probit to dprobit to interpretation

From   <[email protected]>
To   <[email protected]>
Subject   st: From probit to dprobit to interpretation
Date   Fri, 11 Jan 2008 13:52:10 +0100

I have a general question about how to interpret and use probabilities
from a probit model I have esimated in Stata. 

I have estimated a probit model where n=1000 000 customers with only 1
independent dummy variable (x) (for the sake of clarity), and get the
following estimated coefficients:

y_pred=-2.33-0.431*x (x being significant)

No the way I understand this is that these coefficients, except for the
signs and significance level, is hard to interpret. Thus, I can derive
it as a probability model, and then again calculate probabilities from
any table with standard cumulative normal distribution values. Turning
on and off x will give me the discrete change, thus

Turning off the effect of X thus gives me:
y_pred=-2.33-(0.431*0) and

Tuning on the effect
y_pred=-2.33-(0.431*1)=-2.761 and

The difference between these probabilities is the discrete change, and
this change can be directly estimated using a dprobit model in Stata?
Discrete change=0.99-0.29=-0.7%

Most textbooks stops here, and I think that so far I am on the right
track - but I want to interpret this probability in terms of what this x
induced effect means in terms of my sample...

In this particular model my sample is 1000000, and x=1 is a membership
program of which there are 500000 members. Would it be correct to assume
that the discrete change estimated above in terms of customers could be
interpreted as following:

Turning of the effect of X:

Turning on the effect of X:

Then, the way I have understood this:
Discrete change, reduction induced by x=9900-2900=7000?

Any help would be greatly appreciated.

Best wishes,
Alexander Severinsen

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