Identifying break points

[Anton-24]

Dear Listers,

A colleague of mine has uncovered a curvilinear relationship (linear,
quadratic & cubic terms are all significant) between organizational revenue
and another continuous variable. She is now interested in identifying
turning or breaking points.  That is, identifying the revenue point(s) where
this other variable seems to change.

Back in 2006, Jan Spousta recommended using decision trees for this type of
analysis.  Unfortunately, our office does not have this module.  Are there
other procedures that may help, other than visually identifying such points?

Your suggestions are much appreciated.

Anton

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Hector Maletta]

Are there actually "break" points or is there a smooth curve? I wonder
whether the cubic function smoothly fits the data, or there are large
variability and residuals, or "jumps" along the way.
In the case of a reasonable good fit, or some theoretical reason to believe
that a cubic function could reflect some underlying causal process, one
could use the first and second derivatives of the fitted function, i.e. the
points where the curve changes direction (first derivative), say from
increasing to decreasing, or reaches an inflection point in which it changes
from decelerating to accelerating or the reverse (second derivative). The
points where the derivatives equal zero (and probably change sign) are the
crucial points. The first derivative of a cubic function is a quadratic one,
and the second derivative is a linear function, so mathematically the
problem is easy.
A different approach is using ROC curves to identify the points.

Hector

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Anton
Sent: 30 October 2008 13:17
To: [hidden email]
Subject: Identifying break points

Dear Listers,

A colleague of mine has uncovered a curvilinear relationship (linear,
quadratic & cubic terms are all significant) between organizational revenue
and another continuous variable. She is now interested in identifying
turning or breaking points.  That is, identifying the revenue point(s) where
this other variable seems to change.

Back in 2006, Jan Spousta recommended using decision trees for this type of
analysis.  Unfortunately, our office does not have this module.  Are there
other procedures that may help, other than visually identifying such points?

Your suggestions are much appreciated.

Anton

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Peck, Jon]

First, I would think about the goal.  Usually breakpoints are appropriate when there is some sort of structural shift that might occur, and you are trying to locate it.  If you just need a flexible form for the response function, looking for breakpoints may not be the best way to proceed.  The CURVEFIT base procedure will estimate a wide variety of models that are nonlinear in the variables to help you pick.

A much cooler way to go is to use CATREG, which is in the Categories option, to estimate optimal transformations of the predictor(s).  The transformation plots are particularly useful.

HTH,
Jon Peck

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Anton
Sent: Thursday, October 30, 2008 9:17 AM
To: [hidden email]
Subject: [SPSSX-L] Identifying break points

Dear Listers,

A colleague of mine has uncovered a curvilinear relationship (linear,
quadratic & cubic terms are all significant) between organizational revenue
and another continuous variable. She is now interested in identifying
turning or breaking points.  That is, identifying the revenue point(s) where
this other variable seems to change.

Back in 2006, Jan Spousta recommended using decision trees for this type of
analysis.  Unfortunately, our office does not have this module.  Are there
other procedures that may help, other than visually identifying such points?

Your suggestions are much appreciated.

Anton

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD