What you say is correct and there is no contradiction between all these
statements. From a probit model you can derive predicted proportions,
and with predicted proportions you can derive predicted counts in your
sample (and if you know the size of your population the predicted
counts in your population).
Hope this helps,
Maarten
--- [email protected] wrote:
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
Pr(z<2.33)=0.99%
Tuning on the effect
y_pred=-2.33-(0.431*1)=-2.761 and
Pr(z<2.761)=0.29%
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:
0.99%*1000000=9900
Turning on the effect of X:
0.29%*1000000=2900
Then, the way I have understood this:
Discrete change, reduction induced by x=9900-2900=7000?
-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands
visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434
+31 20 5986715
http://home.fsw.vu.nl/m.buis/
-----------------------------------------
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