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I am trying to calculate the wealth index of a rural community of Nepal. For this, I used 10 household assets variables after conducting a descriptive analysis. I used the principal component analysis. I got the first four components have more than 1 eigenvalue, those four component explains 54% of the variance (the first component explains only 17.9%). The KMO measure of sampling adequacy is 0.619, Bartlett's test of sphericity is <0.001. Now, I am confused about the following things:

  1. Does the wealth index create (by predict command) considers all component those eigenvalue is more than 1 or just the first component? If it is only the first component then, does it means it only explains 17.9% variance?
  2. If I add one more variable, it increases the total variance, Bartlett's test remains significant, but KMO measure drops to 0.599. Can we consider KMO 0.599 as 0.6 (as 0.6 is the minimum acceptable value)? Can I proceed with my study with the above results? Sorry If my question is not clear, I can explain it further if you want. Thank you
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  • $\begingroup$ Thank you very much @Fcold, it's very much helpful. So, for example: 4 components which eigen value is more than 1, explains vairance as following comp1: 20 %, comp2:14%, comp3:12%, comp4: 10%. So if wealth index is created it considers first component, but while reporting, can we say our model explains 56% or just 20%. Thank you, I hope, I am not bothering you 😊 $\endgroup$
    – Prasant Shahi
    Commented Jul 19, 2020 at 4:33

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Not sure about your second question. You are still at the limit of KMO test, on the other hand, if those new variables make theoretical sense, I would go ahead and include them. Regarding the first question. the short answer is no. If you do the following:

pca x1 x2 x3 x4 x5
predict index1

the "index1" will consider only the first component, which is the idea behind a wealth index. The other components you are interested in could be used perhaps for a multidimensional index that captures different dimensions of wealth.

HTH

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  • $\begingroup$ Thank you very much @Fcold, it's very much helpful. So, for example: 4 components which eigen value is more than 1, explains variance as following comp1: 20 %, comp2:14%, comp3:12%, comp4: 10%. So if wealth index is created it considers the first component, but while reporting, can we say our model explains 56% or just 20%. Thank you, I hope, I am not bothering you 😊 $\endgroup$
    – Prasant Shahi
    Commented Jul 19, 2020 at 22:17
  • $\begingroup$ Just 20%, because that is how much the first component explains. $\endgroup$
    – Fcold
    Commented Jul 20, 2020 at 23:02
  • $\begingroup$ Thank you very much :) @Fcold $\endgroup$
    – Prasant Shahi
    Commented Jul 21, 2020 at 8:44

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