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

 From Shikha Sinha To statalist@hsphsun2.harvard.edu Subject Re: st: wealth score using principal component analysis (PCA) Date Tue, 25 Sep 2012 16:22:51 -0700

```Thanks for your response Nick and stat!

I think I am struggling with how to create one scores from two
components. Let me pose my question again.

Suppose I want to create one index out of six variables. For example,
I want to create a  "women autonomy index". The index would be one
number for every households. The Demographic and health survey (DHS)
using the information in all the 10 questions, I just want to use an
index that contains the summary information of all the 10
questions/variables. I can use -pca to create the index. Once I use
-pca x1-x10, I can choose number of principal components (pc) to
retain based on eigenvalues or screeplot. Let assume that there are
three pc that have eigenvalues > 1 and I want to retain all these
components, though the first component has the highest variation.

Now, I want to create a "women autonomy index" based on these three
pc. How can I do that? If I use -predict p1 p2 p3, scores; it gives
three different scores, all unrelated. However, I want just one index,
kindly suggest how to do this.

Thanks,
Shikha

On Tue, Sep 25, 2012 at 9:05 AM, Stas Kolenikov <skolenik@gmail.com> wrote:
> Regarding (c), you would be best off with a structural equations model
> (-sem- module), and forgo the PCA whatsoever.
>
> --
> -- Stas Kolenikov, PhD, PStat (SSC)  ::  http://stas.kolenikov.name
> -- Senior Survey Statistician, Abt SRBI  ::  work email kolenikovs at
> srbi dot com
> -- Opinions stated in this email are mine only, and do not reflect the
> position of my employer
>
>
>
> On Mon, Sep 24, 2012 at 7:07 PM, Nick Cox <njcoxstata@gmail.com> wrote:
>> 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
>> 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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```