I plan to create social vulnerability index using survey data. Principal component analysis was recommended by several authors. I am looking for clear and step-by-step process of doing this. I have access to SPSS and STATA. Your reply will be highly appreciated.
Principal component analysis PCA involves the analysis of the variance -covariance matrix or the correlation matrix of the set of variables. Eigenvalues of the matrix are calculated and arranged on order of magnitude. The first principal component is associated with the largest eigenvalue, the second with the second largest and so on. For PCA I recommend minitab.
You can do it in SPSS. The Help menu has some step-by-step examples, although it's best to familiarize with PCA elsewhere beforehand. You should become familiar with the overall procedural concept of PCA and some of the terminology it uses, and the steps (such as rotation) to optimize your results. You might also find a published paper that used PCA in the analysis and work backwards, with the goal of eventually being able to understand all the terminology and procedures that are in the paper.
The pitfalls of PCA are that the results can sometimes be hard to interpret. PCA is one of several "factor analysis" methods that seek to group concepts or domains that are similar to each other. For example, a survey asking about chronic illness in people might be analyzed with PCA to reveal that participants' concerns about employment and social ties cluster together, or that (poor) health and (lack of) recreational activity cluster together. These two clusters or factors could then be identified as a "social status" factor and an "activity impairment" factor that would separate the chronically ill people from the non-chronically ill. That's just an example, but it will be up to you to name and interpret these clusters or factors that result from the PCA analysis. They should make sense conceptually and, ideally, fit in with other establilshed theories, for example about health and illness. The factors you identify can also be further tested with other analyses on the same or different datasets. The pitfalls are that sometimes these identified factors (also called clusters or domains) can be argued to mean different things by different people.
Another potential pitfall is that your data may not be suitable for PCA because of the way it is coded. You may have to transform some of your variables to make them suitable for the PCA procedure so the PCA will work and make sense.
But PCA is a good tool to simplify a lot of survey questions into a few simple domains or factors of interest.
Thanks a lot everyone, for your suggestions. I have started reading some relevant journal articles on PCA.
You can use JMP (SAS) software. It is easy to use and interpret with tutorial for beginners at the home page. A free trial version is available online. PC1 and PC2 have the larger variation of the overall data set. Additionally, PCs with eigen value > 1 are considered and retained for detailed explanation of the total variation in the entire data set.
The most complete (and easy) software in my opinion is SPSS which allows several options for PCA.Moreover there is a very interesting book written by Andy Field (Field, A.,2013. Discovering statistics using IBM SPSS statistics. Sage).
But the manage of big data with SPSS is not easy like using STATA do file. Graphically, in order to represent the factorial plans, the best software is DECISIA SPAD. Unfortunatelly I think that this software is not availbe anymore. Moreover the manage of data using SPAD is very annoyng.
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