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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Thu, 27 Sep 2012 09:26:14 +0100 |

I can't give an answer to this question that is likely to satisfy you. PCA and SEM are very different methods. PCA is in my view primarily a multivariate transformation technique. SEM is, more obviously, a family of modelling techniques. Even in this thread the use of PCA appears to be part of a wider model-based strategy and that is likely to be typical of most projects in which it appears. I don't think "use PCA" is ever likely to be the core of the answer to "what should I do?" but "use SEM" might be, sometimes. Stas [sic] can speak for himself, but I suspect his position would be close to mine on this. Nick On Thu, Sep 27, 2012 at 8:06 AM, 汪哲仁 <chejen.wang@gmail.com> wrote: > Dear Nick and Stat, > > May I ask a question? In which circumstances, the PCA is a better > choice than SEM? 2012/9/27 Nick Cox <njcoxstata@gmail.com> >> You are confusing two different questions. Throughout I focus on the >> case you are looking at where PCA is based on the correlation matrix. >> >> If the aim is to use the most important PC, then that is labelled 1, >> but even if it weren't we could identify it by its having the largest >> eigenvalue attached and no extra considerations arise. >> >> If the aim is to identify which PCs are "important" or "worthy of use" >> (typically one or more) and should be used in later analyses, then >> this is necessarily a looser, more open question and the best art is a >> darker matter. There can't be an answer independent of what you are >> trying to do. Some people do stress a rule of thumb such as >> eigenvalues > 1 and some people look for a break in the eigenvalues >> using a scree plot. In some projects PCs that are used later are good >> if interpretable as having high correlations with particular >> variables; in other projects the PCs are just composite variables with >> the properties assigned to them and interpretability is less material. >> >> Every book I know on PCA stresses this open aspect of the method. The >> books by Jolliffe and Jackson referenced in the -pca- documentation >> certainly do. >> >> It's not clear exactly why you feel committed in advance to using PCA >> like this. I sympathise with the advice given earlier by Stas >> Kolenikov to consider something more like an SEM. >> >> Nick >> >> On Wed, Sep 26, 2012 at 9:33 PM, Shikha Sinha <shikha.sinha414@gmail.com> wrote: >> > Ok, I got it now that if I want to use one score, then PC1 is the most >> > relevant one, and then for further distinction between financial vs >> > social, we need to look at factor loadings in each PC2, PC3 , to >> > figure out if PC2 is better than PC1 if the focus is on social or >> > financial autonomy. >> > >> > Then I am struggling to understand the use of selecting components >> > based on eigenvalues. What is the use of selecting PC based either on >> > eigenvalues or screeplot, if we are always (most of the time) going to >> > use the 1st component. An example on the importance of eigenvalues in >> > selecting components would be very helpful ( or any ref.) * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: wealth score using principal component analysis (PCA)***From:*Stas Kolenikov <skolenik@gmail.com>

**References**:**st: wealth score using principal component analysis (PCA)***From:*Shikha Sinha <shikha.sinha414@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Stas Kolenikov <skolenik@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Shikha Sinha <shikha.sinha414@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Stas Kolenikov <skolenik@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Shikha Sinha <shikha.sinha414@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: wealth score using principal component analysis (PCA)***From:*汪哲仁 <chejen.wang@gmail.com>

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