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Re: st: interpreting probit estimates
At 02:02 PM 2/15/2006, Jonathan A. Schwabish wrote:
This may or may not be a Stata question. I am trying
to convert probit estimates to the following
interpretation: "A standard deviation increase in the
[independent variable] increases the [dependent
variable] by x% (or x standard deviations)."
The -listcoef- command is very useful but for
interpretation purposes, is only applicable to the
logit command (log odds). Does anyone know of a Stata
command, or just a way to modify probit results, to
fit this type of interpretation?
To follow up a bit on my previous answer: In binary probit, the error
term is assumed to be distributed normally with variance 1. In
binary logit, the error term is assumed to be distributed
logistically with variance (pi^2)/3 = roughly 3.29. For the most
part though, these distributions are very similar, differing mostly
by a scale factor (hence the widespread claim that it usually doesn't
matter that much whether you use logit or probit).
Before standardization, the estimated V(Y*) = V(XB) + V(error term)
where the variance of the error term is as described above. After
Y-standardization, V(Y*) = 1
Note what happens when you standardize probit and then logit coefficients:
. use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";
(77 & 89 General Social Survey)
. quietly probit warmlt2 yr89 male white age ed prst
. listcoef, std
probit (N=2293): Unstandardized and Standardized Estimates
Observed SD: .33585294
Latent SD: 1.0785709
-------------------------------------------------------------------------------
warmlt2
| b z P>|z| bStdX bStdY bStdXY SDofX
-------------+-----------------------------------------------------------------
yr89
| -0.51003 -6.517 0.000 -0.2498 -0.4729 -0.2316 0.4897
male
| 0.16937 2.439 0.015 0.0845 0.1570 0.0783 0.4989
white
| 0.28195 2.382 0.017 0.0928 0.2614 0.0860 0.3290
age
| 0.00920 4.223 0.000 0.1544 0.0085 0.1432 16.7790
ed
| -0.05786 -4.207 0.000 -0.1829 -0.0536 -0.1696 3.1608
prst
| 0.00066 0.221 0.825 0.0095 0.0006 0.0088 14.4923
-------------------------------------------------------------------------------
. quietly logit warmlt2 yr89 male white age ed prst
. listcoef, std
logit (N=2293): Unstandardized and Standardized Estimates
Observed SD: .33585294
Latent SD: 1.9615163
Odds of: SD vs D,A,SA
-------------------------------------------------------------------------------
warmlt2
| b z P>|z| bStdX bStdY bStdXY SDofX
-------------+-----------------------------------------------------------------
yr89
| -0.96474 -6.256 0.000 -0.4725 -0.4918 -0.2409 0.4897
male
| 0.30536 2.364 0.018 0.1523 0.1557 0.0777 0.4989
white
| 0.55266 2.397 0.017 0.1818 0.2818 0.0927 0.3290
age
| 0.01647 4.060 0.000 0.2764 0.0084 0.1409 16.7790
ed
| -0.10480 -4.136 0.000 -0.3312 -0.0534 -0.1689 3.1608
prst
| 0.00141 0.249 0.803 0.0205 0.0007 0.0104 14.4923
-------------------------------------------------------------------------------
The columns labeled bStdY and bStdXY (in which Y* is standardized in
both cases) are pretty much identical to each other. So, the fact
that you are using probit rather than logit really shouldn't make the
task of interpretation all that much harder.
The latest edition of Long and Freese can be found at
http://www.stata.com/bookstore/regmodcdvs.html
Long's 1997 book is also good for providing a more in-depth
mathematical discussion of these and other issues:
http://www.stata.com/bookstore/regmod.html
Also, I show some more formal calculations at
http://www.nd.edu/~rwilliam/xsoc694/x03.pdf
-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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EMAIL: [email protected]
WWW (personal): http://www.nd.edu/~rwilliam
WWW (department): http://www.nd.edu/~soc
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