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Re: st: wealth score using principal component analysis (PCA)


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: wealth score using principal component analysis (PCA)
Date   Tue, 25 Sep 2012 01:07:27 +0100

You seem to be misunderstanding both PCA and the syntax of -predict-
after -pca-.

To take the second first, -predict- just gives you as many components
as you ask for. Ask for one by giving one variable name and you get
scores for the first PC, regardless of what name you give. Stata's
indifferent to what name you give (so long as it is new and legal) and
indeed

predict p3
predict p777

would give you further identical copies of the first PC.

predict P1 P2

would give you scores for the first two PCs.

As for PCA there are potentially as many PCs as variables: although
the -components()- option puts a self-defined limit on how many you
can calculate the main purpose of this option appears to be to let
-pca- behave more like -factor-.

Even if your purpose is to use just one PC, it usually makes sense to
look at several and the relationships of those PCs to your original
variables. Sometimes the second, third, ... PC pick up important parts
of the variation and it is a good idea to look at those too to see
what the first PC is missing. In the case of wealth variables it might
be a good idea to think about using PCA on logarithmic transformations
of the variables too (assuming all values are strictly positive).

Note that the audience of Statalist is very international and
interdisciplinary, so that assuming that "DHS" is self-evident is
likely to be wrong in many cases.

Your last question (c) is unanswerable. Many people do it, but how far
it is "OK" in your project depends on your goals and your data, which
we can't see.

Nick

On Mon, Sep 24, 2012 at 9:20 PM, Shikha Sinha <shikha.sinha414@gmail.com> wrote:

> I am trying to create a wealth score using the ownership of different
> assets in the DHS survey.  I am suing -pca but I am not sure how to
> estimate the score as I want to use the wealth score as one of the
> independent variables.
>
> pca x1-x4
> predict p1,score
>
> but -predict only generates score from first component.
>
> I also tried the following,
>
> -pca x1-x4, components (2)
> predict p2, score
>
> However, p1 and p2 are same.
>
> My questions are, (a) why there is no difference between p1 and p2?
> (b) How can I generate score by using first 2 components only?
> (c) Is it ok to use continuous pca score as an independent variable?
>
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