Inknots and splines

[Bob Schacht-3]

My introduction to factor analysis was several decades ago.
I need to use CATPCA, but there is a lot of new terminology that makes
little sense to me.  Can someone please explain what InKnots and splines
are, or refer me to a website with a beginner's level explanation? Yes, I
know that inknots refers to
>"The number of interior knots. The minimum is 0, and the maximum is the
>number of categories of the variable minus 2. If the specified value is
>too large, the procedure adjusts the number of interior knots to the
>maximum. The default number of interior knots is 2."

But you might just as well say, "Twas brillig, and the slithey toves did
gyre and gimble in the wabe" or words to that effect.

Thanks,
Bob

Robert M. Schacht, Ph.D. <[hidden email]>
Pacific Basin Rehabilitation Research & Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814

=====================
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

[Kooij, A.J. van der]

The spline scaling levels result in a transformation curve that is smoother than the ordinal and nominal transformations, which are step functions.

The smoothness of the transformation curve (and thereby the DF) depends on the number of interior knots and the degree of the spline: more knots and higher degree -> more DF and less smooth curve.

DF spline transformation: number of interior knots + degree.

DF nominal step transformation: number of categories minus 1.

DF ordinal step transformation: number  of categories with different quantified values minus 1.

Thus, spline transformation is suited for variables with large number of categories (and especially for transformation of numeric variables that you do not want to bin, so number of "categories" equal to number of cases or number of distinct values of the variable).

 

With 0 interior knots and 1 degree, the transformation is linear (= numeric scaling level).

When the number of interior knots is equal to the number of categories minus 2, the nominal/ordinal spline transformation is equal to the nominal/ordinal step transformation. So, depending on the number of knots and degree, nominal/ordinal spline transformation is somewhere in between linear transformation (1 DF, most smooth)  and nominal/ordinal step transformation (DF depends on number of categories, least smooth).

 

More detail and graphical illustrations:

page 16-22 of chapter 2 at https://openaccess.leidenuniv.nl/dspace/handle/1887/12386 (CATPCA) and

page 5-7 of chapter 1 at https://openaccess.leidenuniv.nl/dspace/handle/1887/12096 (CATREG)

 

Regards,

Anita van der Kooij

Data Theory Group

Leiden University

 


________________________________

From: SPSSX(r) Discussion on behalf of Bob Schacht
Sent: Fri 03/10/2008 22:48
To: [hidden email]
Subject: Inknots and splines



My introduction to factor analysis was several decades ago.
I need to use CATPCA, but there is a lot of new terminology that makes
little sense to me.  Can someone please explain what InKnots and splines
are, or refer me to a website with a beginner's level explanation? Yes, I
know that inknots refers to
>"The number of interior knots. The minimum is 0, and the maximum is the
>number of categories of the variable minus 2. If the specified value is
>too large, the procedure adjusts the number of interior knots to the
>maximum. The default number of interior knots is 2."

But you might just as well say, "Twas brillig, and the slithey toves did
gyre and gimble in the wabe" or words to that effect.

Thanks,
Bob

Robert M. Schacht, Ph.D. <[hidden email]>
Pacific Basin Rehabilitation Research & Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814

=====================
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



**********************************************************************
This email and any files transmitted with it are confidential and
intended solely for the use of the individual or entity to whom they
are addressed. If you have received this email in error please notify
the system manager.
**********************************************************************



====================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