# Re: SV: st: From probit to dprobit to interpretation

 From Maarten buis <[email protected]> To [email protected] Subject Re: SV: st: From probit to dprobit to interpretation Date Fri, 11 Jan 2008 15:11:04 +0000 (GMT)

```The separate probabilities need to be applied to their group, but the
discrete change needs to be applied to the total sample.

--- [email protected] wrote:

> 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,
> Alexander
>
> -----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,
> 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
>
> Buitenveldertselaan 3 (Metropolitan), room Z434
>
> +31 20 5986715
>
> http://home.fsw.vu.nl/m.buis/
> -----------------------------------------
>
>
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-----------------------------------------
Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

http://home.fsw.vu.nl/m.buis/
-----------------------------------------

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