Date:         Tue, 28 Jun 2005 19:44:57 +0200
Reply-To:     "Kooij, A.J. van der" <KOOIJ@fsw.leidenuniv.nl>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         "Kooij, A.J. van der" <KOOIJ@fsw.leidenuniv.nl>
Subject:      Re: Question about Nonlinear Principal Component Analysis
Content-Type: text/plain; charset="us-ascii"

Answers to Questions:

1.Is the PCA literature applicable in practical terms (e.g. factor
loadings <0.30 shall be ignored etc.).
Yes, loadings, eigenvalues, vaf, etc. can be interpreted as for linear
PCA (because in Nonlinear Principal Component Analysis the model is the
same as the linear PCA model; the nonlinearity is in the transformations
of the variables)

2.If not, is there hands-on literature about NPCA? So far I have only
identified the SPSS Categories manual (11.0), which assumes prior
knowledge about the suitability of this technique (other literature is
either theoretically oriented, or deals with very special alternatives
to NPCA, not included in SPSS, or not Gifi 1991).
Meulman, J.J., Van der Kooij,. A.J., & Heiser, W.J. (2004). Principal
Components Analysis with Nonlinear Optimal Scaling Transformations for
Ordinal and Nominal Data. In: D. Kaplan (ed.), Handbook of Quantitative
Methods in the Social Sciences, (pp. 49-70). Newbury Park, CA: Sage
Publications.

3.I may only have 40 cases (observations) and 4 variables. I am aware
that this is not ideal, but is it definitely too low?
No, not for exploratory purposes.

4.Is it possible to use dummies (only two classes), or do they provide
too low variation?
If with dummies you mean binary variable, is okay (note that with binary
variable no matter what scaling level you choose, the transformation is
always the same as with numerical scaling level)

Any help would be extremely welcome
You can always mail me off-line if you need any more help.

Anita van der Kooij
Data Theory Group
Leiden University

-----Original Message-----
From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU] On Behalf Of
P.M.J. Stromberg
Sent: 28 June 2005 17:12
To: SPSSX-L@LISTSERV.UGA.EDU
Subject: Question about Nonlinear Principal Component Analysis


Dear list participants,

I plan to use Nonlinear Principal Component Analysis as an input to a
regression analysis. Specifically, to identify variables (ordered) that
I will use to construct an index, which I plan to include as an
independent variable in a logit regression. I am using ordered variables
coded in 3 or 4 classes, to create an index of the level of uncertainty
in contracting. For example one of the input variables represents
organisational complexity: (1)government, (2)local community, (3)both
government and local community.

Questions:

1.Is the PCA literature applicable in practical terms (e.g. factor
loadings <0.30 shall be ignored etc.).

2.If not, is there hands-on literature about NPCA? So far I have only
identified the SPSS Categories manual (11.0), which assumes prior
knowledge about the suitability of this technique (other literature is
either theoretically oriented, or deals with very special alternatives
to NPCA, not included in SPSS, or not Gifi 1991).

3.I may only have 40 cases (observations) and 4 variables. I am aware
that this is not ideal, but is it definitely too low?

4.Is it possible to use dummies (only two classes), or do they provide
too low variation?

Any help would be extremely welcome

Thank you very much.

Best wishes,
Per Stromberg

Per Stromberg
Researcher
Department of Land Economy
University of Cambridge
United Kingdom
Website: www.landecon.cam.ac.uk
E-mail: pmjs2@cam.ac.uk
Tel: 0044 (01223) 336250
Fax: 0044 (01223) 336086

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