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SV: st: From probit to dprobit to interpretation

From   <[email protected]>
To   <[email protected]>
Subject   SV: st: From probit to dprobit to interpretation
Date   Fri, 11 Jan 2008 15:01:52 +0100

Thanks Maarten! That is very helpful. I guess what have been confusing for me then is how to apply the predicted -0.7% discrete change (the difference between turning on and off the effect), on the full sample as I have done below, or only on those 500000 that are signed up to the membership program. The difference offcourse making a huge impact on the result.

Best wishes,

-----Opprinnelig melding-----
Fra: [email protected] [mailto:[email protected]] P� vegne av Maarten buis
Sendt: 11. januar 2008 14:16
Til: stata list
Emne: RE: st: From probit to dprobit to interpretation

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,

--- [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

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?

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

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