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RE: st: How to implement Discrete Principal Component Analysis by using POLYCHORICPCA


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: How to implement Discrete Principal Component Analysis by using POLYCHORICPCA
Date   Thu, 5 Jan 2012 18:19:12 -0500

Hi Charles,

Sorry, I'm so used to the term "loadings" that your post initially confused me, but now I think I've shaken it off. :)

Are you sure you're not missing a piece of code somewhere? I don't know why you wouldn't get the eigenvectors, as those should be standard output for any PCA or FA. If Stas K. is listening in, he could probably comment further if you displayed the input code.

I will add one question, however: Are you sure that all of the relationships in the data are linear? I have my doubts... researchers would do well to exploit NL-PCA more often:

Linting, M., Meulman, J.J., Groenen, P.J.F., & van der Koojj, A.J. (2007). Nonlinear Principal Components Analysis: Introduction and Application. Psychological Methods, 12(3), 336-358.

Lavado, N., & Calapez, T. (2011). Quasi-Linear PCA: Low Order Spline’s Approach to Non-Linear Principal Components. Proceedings of the World Congress on Engineering 2011, Vol I,July 6-8, 2011. London, UK. http://www.iaeng.org/publication/WCE2011/WCE2011_pp360-364.pdf

Ferrari, P.A., Annoni, P., Barbiero, A., & Manzi, G. (2011). An imputation method for categorical variables with application to nonlinear principal component analysis. Computational Statistics & Data Analysis, 55(7), 2410-2420.

Cam


----------------------------------------
> Date: Fri, 6 Jan 2012 01:35:28 +0400
> Subject: Re: st: How to implement Discrete Principal Component Analysis by using POLYCHORICPCA
> From: chejen.wang@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> Dear Cam,
>
> Thanks for your reply. Usually, pca procedure give us a
> result like this.
> =================================================================================
> pca foreign rep78 mpg
>
> Principal components/correlation Number of obs = 69
> Number of comp. = 3
> Trace = 3
> Rotation: (unrotated = principal) Rho = 1.0000
>
> --------------------------------------------------------------------------
> Component | Eigenvalue Difference Proportion Cumulative
> -------------+------------------------------------------------------------
> Comp1 | 1.9703 1.34377 0.6568 0.6568
> Comp2 | .626528 .223359 0.2088 0.8656
> Comp3 | .403169 . 0.1344 1.0000
> --------------------------------------------------------------------------
>
> Principal components (eigenvectors)
>
> ----------------------------------------------------------
> Variable | Comp1 Comp2 Comp3 | Unexplained
> -------------+------------------------------+-------------
> foreign | 0.6084 -0.2732 -0.7451 | 0
> rep78 | 0.5910 -0.4706 0.6551 | 0
> mpg | 0.5296 0.8390 0.1249 | 0
> ----------------------------------------------------------
>
> ===================================================================================
> but polychoricpca only give us results without eigenvectores, like below.
> polychoricpca foreign mpg rep78
>
> k | Eigenvalues | Proportion explained | Cum. explained
> ----+---------------+------------------------+------------------
> 1 | 2.206757 | 0.735586 | 0.735586
> 2 | 0.615445 | 0.205148 | 0.940734
> 3 | 0.177798 | 0.059266 | 1.000000
>
>
> My question is that, after running polychoricpca procedure, how can I
> know the eigenvectors to construct an index.
>
>
> Thanks for your attention.
>
>
>
> with kind regards,
>
>
> Charles Wang
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