mahalanobis distance/syntax

[Anthony Petrosino]

Hello SPSS Users~

We are looking to solve the following.

In the context of an evaluation of an educational policy, we are using
Mahalanobis Distance (M/D) to help us in matching 46 comparison schools to
23 treatment schools, from a total pool of 411 schools.

We have two variables we are looking to compute M/D for, producing it for
each case in our data set. These variables are a sociodemographic
composite index (SCI) and an estimate of true academic performance
(essentially, math scores minus the SCI).

Has anyone ever computed M/D in SPSS for just two variables? We know that
SPSS provides the menu driven selection for M/D for regression and some of
the classification techniques, but it does not seem to fit what we are
looking for.

We have run a procedure in STATA, and used the following syntax:

_____________
*Compute Mahalanobis Distance
matrix drop _all
mkmat scix true, matrix(xvar)
matrix accum cov = scix true, noc dev
matrix cov = cov/(r(N)-1)
matrix factorx= (xvar) * (inv(cov)) * (xvar')
matrix factor= (vecdiag(factorx))'
svmat factor, names(factor)
--------------
We would like to learn how to do something similar in SPSS to validate
these findings.  Like STATA, I suspect this is something that we need
special syntax for, and any clues to this will be greatly appreciated.

Sincere thanks in advance--
Anthony


Anthony Petrosino, Ph.D.
Senior Research Associate,
Learning Innovations at WestEd &
Associate Director of Research, Regional Educational Laboratory, Northeast
and Islands (REL-NEI)
200 Unicorn Park Drive, 4th floor
Woburn, MA 01824 USA
781-481-1117

[Della Mora, Marcelo]

Hello Anthony

I understand the broad concept: the probability that a case belongs to a
particular group is basically proportional to the Mahalanobis distance
from that group centroid.  However it is not exactly proportional
because we assume a multivariate normal distribution around each
centroid.

This suggests to me the particular calculations are pretty complex!

So, I'm sorry not to answer your question in full, but if you happen to
get a good reply on this could you forward it on to me?

Many thanks,
Marcello




Marcello Della Mora
Citibank LATAM Decision Management
[phone]
[hidden email]



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Anthony Petrosino
Sent: Monday, February 05, 2007 9:47 PM
To: [hidden email]
Subject: mahalanobis distance/syntax


Hello SPSS Users~

We are looking to solve the following.

In the context of an evaluation of an educational policy, we are using
Mahalanobis Distance (M/D) to help us in matching 46 comparison schools to
23 treatment schools, from a total pool of 411 schools.

We have two variables we are looking to compute M/D for, producing it for
each case in our data set. These variables are a sociodemographic
composite index (SCI) and an estimate of true academic performance
(essentially, math scores minus the SCI).

Has anyone ever computed M/D in SPSS for just two variables? We know that
SPSS provides the menu driven selection for M/D for regression and some of
the classification techniques, but it does not seem to fit what we are
looking for.

We have run a procedure in STATA, and used the following syntax:

_____________
*Compute Mahalanobis Distance
matrix drop _all
mkmat scix true, matrix(xvar)
matrix accum cov = scix true, noc dev
matrix cov = cov/(r(N)-1)
matrix factorx= (xvar) * (inv(cov)) * (xvar')
matrix factor= (vecdiag(factorx))'
svmat factor, names(factor)
--------------
We would like to learn how to do something similar in SPSS to validate
these findings.  Like STATA, I suspect this is something that we need
special syntax for, and any clues to this will be greatly appreciated.

Sincere thanks in advance--
Anthony


Anthony Petrosino, Ph.D.
Senior Research Associate,
Learning Innovations at WestEd &
Associate Director of Research, Regional Educational Laboratory, Northeast
and Islands (REL-NEI)
200 Unicorn Park Drive, 4th floor
Woburn, MA 01824 USA
781-481-1117