Date:         Thu, 2 Jul 1998 16:15:49 -0500
Reply-To:     "Nichols, David" <nichols@SPSS.COM>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         "Nichols, David" <nichols@SPSS.COM>
Subject:      Re: Non Linear Relationships and Factor Analysis
Comments: To: Joel KADDOUR <kaddour@CLSH.U-NANCY.FR>

Nonlinear principal components analysis in PRINCALS in SPSS allows multiple
options for the measurement levels of the variables, but it's really for
categorical data (the values have to be positive integers). The ALSCAL
multidimensional scaling procedure also allows the ability to specify
interval or ratio as the measurement level, though only for dissimilarity
data. SPSS does not have a nonlinear factor analysis procedure.
 
David Nichols
Principal Support Statistician and
Manager of Statistical Support
SPSS Inc.
 
----------
From:  Joel KADDOUR [SMTP:kaddour@CLSH.U-NANCY.FR]
Sent:  Wednesday, June 17, 1998 6:32 AM
To:  SPSSX-L@UGA.CC.UGA.EDU
Subject:  Non Linear Relationships and Factor Analysis
 
To study relationships between variables that are Non Linear Related we
can
use Non Linear Regression or Linear regression if this relation can be
linearized (f.i. Log-Linear or Power models).
 
Usually to extract a latent variable or a component we can use Factor
Analysis or Principal Components Analysis. But in this two models
equations
are linear.
 
1) How does PCA or FA deals with curvilinear relationships, it seems
difficult to linearize relationships between two variables without
curvilinearizing (sorry for this ugly word) the relations with other
variables.
 
A solution is to use other models to study the structure such as
MultiDimensional Scaling, or Non Linear Principal Components Analysis, but
doing this, i loose benefits of metrics property of my measure (scores at
subtests).
 
2) Can I extract factors or principal components from variables that are
curvilinear related, keeping metrics property of my measure ?
 
Errors certainly occured in this line, references of articles are welcome
(not for my poor english but for Non Linear Relationships )!
 
Regards
 
 
 
 
         Joel KADDOUR
Groupe d'Analyse Psychometrique
    des COnduites (GRAPCO)
      Universite Nancy 2
          B.P. 33-97
     F - 54015 Nancy Cedex
     kaddour@clsh.u-nancy.fr