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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Heteroskedastic Probit Model |

Date |
Thu, 22 Apr 2010 08:57:53 -0700 (PDT) |

--- On Thu, 22/4/10, Mustafa Brahim wrote: > Just a matter of curiosity. How you > know it is not there in the first > place? that's exactly what I want to understand. It may be easiest to start with a case where such information is present: Say we want to know what the "effect" of being a foreign (non-US) or domestic (US) car on the price. We might type: sysuse auto, clear reg price foreign we find an "effect" of foreign that is $312.26. The information for this effect came from the average price within the group of foreign cars and domestic cars: sum price if foreign == 1 local for = r(mean) sum price if foreign == 0 local dom = r(mean) di `for' - `dom' Now we move a bit further away from the data. Say we want to know whether there is heteroskedasticity of the type that the residual variance differs between foreign and domestic cars. What kind of information is then available: We can compute the residuals, that is the difference between the predicted price and the observed price, and than we can compute the variance of these residuals separately for foreign cars and domestic cars: reg price foreign predict yhat gen resid = yhat - price table foreign, c(sd resid) Now we move still a bit further away from the data. We think that there is some latent propensity (y*) in every car for being foreign, and that this latent propensity has the form y* = b0 + b1 mpg + e e is a normally/Gaussian distributed error term, with mean 0 and variance 1. Problem is we don't observe y*, instead we observe foreign: foreign = 1 if y* > 0 foreign = 0 if y* <= 0 So what is the empirical information we have to estimate this model? This model implies a certain relation between the probability of being foreign en mpg, to be precise Pr(foreign==1) = Phi(b0 + b1 mpg), where Phi is the cumulative distribution function of the standard normal distribution. We could also compute the probability for different values of mpg and try out different values of b0 and b1 such that the predicted values are most similar to the observed probabilities. This is the probit model: probit foreign mpg predict pr collapse (mean) pr foreign, by(mpg) scatter pr foreign mpg Notice that the data do not give a lot of information on the exact shape of the relationship (wide scatter). Lets now take yet another step away from the data and move towards the -hekprob- model. The residuals that are being modeled in that model are the difference between the y* and the predicted probability. The problem is that y* is not observed. So what information is present in our data to estimate such a model? Well, if we are willing to assume a certain functional form for the relationship between the variance of e and the some variables, we could use the same trick as with -probit-, but the information we are trying to use then is that these assumptions implie subtle changes in the shape of the relationship between the observed variable and the average (i.e. probability) of foreign, and as we saw in the previous graph, the data contains only very rough information on the shape of that relationship. So that is what I meant when I said that the necesarry information isn't there in the first place. hope this helps, Maarten -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Heteroskedastic Probit Model***From:*Richard Williams <Williams.NDA@comcast.net>

**Re: st: Heteroskedastic Probit Model***From:*Richard Williams <Williams.NDA@comcast.net>

**References**:**Re: st: Heteroskedastic Probit Model***From:*Mustafa Brahim <datotanseri@gmail.com>

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