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Re: st: calculating the confidence intervals for the difference in predicted values


From   Maarten buis <maartenbuis@yahoo.co.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: calculating the confidence intervals for the difference in predicted values
Date   Mon, 19 Oct 2009 02:10:19 -0700 (PDT)

--- On Mon, 19/10/09, stata user wrote:
> The context for this exercise is that, for example, we want
> to study the housing price difference in two regions. I
> first run a regression to determine how the housing
> charateristics (X) would affect a house price (Y), based on
> region A's data. Then I make an out-of-sample prediction of
> house price in region B. And make a in-sample prediction
> of house price in region A. The the difference btw the two
> predictions would be the difference in housing prices between
> region A and region B, if both of the housing prices depend
> on the same set of housing characteristics. 

I would set this up by estimating these comparisons in a single
model using interaction effects, and than use -predictnl- to
compute the differences and ratios:

*----------------------- begin example -----------------------
sysuse auto, clear
gen forXrep78 = foreign*rep78
glm price foreign forXrep78 rep78, link(log)

predictnl diff = exp(xb()) - exp(_b[_cons] + _b[rep78])  ///
    , ci(lb_d ub_d)
predictnl ratio = exp(xb()) / exp(_b[_cons] + _b[rep78]) /// 
    , ci(lb_r ub_r)

sort foreign rep78
list rep78 lb_d diff ub_d if foreign == 1, sepby(rep78)
list rep78 lb_r ratio ub_r if foreign == 1, sepby(rep78)
*------------------------ end example -------------------------
(For more on examples I sent to the Statalist see: 
http://www.maartenbuis.nl/example_faq )

Here I use -glm- with the log link to avoid the problem that
when you log transform the dependent variable, calculate 
predictions, and back transform those prediction again in the
original unit, you won't get the expected price given the 
covariates as the log transformation is a non-linear 
transformation (in fact you will get the conditional geometric 
mean price, rather than the conditional arithmetic mean price).

Hope this helps,
Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------

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