Background: We are studying a rural population of 375 malawian households, and are trying to make an asset index based on a list with over 40 binary (and a few continuous) variables copied from the DHS questionaires for Malawi. Trying to conduct a PCA analysis on this data in STATA I got a really low first principal component value, which only accounts for only about 10-13% of the total variation. Trying the Kaiser-Meyer-Olkin Measure of sampling adequacy (KMO), i get an error and i am told that my matrix is singular.
I further wanted to clean and reduce the data i had to do a better analysis, and excluded variables based on: 1. Whether their frequency was higher or lower than respectively 95% or 5% of the population 2. Whether there were were multicolinear variables, (correlation >90% with other variable), as they probably explain the same variance. 3. If they were significantly (chi square test) correlated with less than 6 other variables 4. If they correlated less than 0,099 with majority of the other variables. After this process i am left with 15 variables, and running the PCA now gives me the output of - PrincipalComponent nr1: 3.42364 - Eigenvalue: 1.93568 - Proportion of explained variance: 0.2282 (22,8%) - KMO: Overall | 0.7385 (according to VAM guide; Minimum acceptable value is a value of 0.6.) - Bartlett test of sphericity: Chi-square= 983.032 Degrees of freedom = 105 p-value = 0.000 H0: variables are not intercorrelated
My questions then are: 1. How can i interpret if the proportion of explained variance is high enough(22,8%), and also the KMO (0,7385)? How important are these measures for the validity of the analysis?
2. Does the criteria i use for exclusion of variables sound reasonable, can i consider anything else when choosing variables? for example look at the strength of the significance level of the correlations instead of the amount of significant values in the correlation matrix? 3. I didn ́t rotate my data as it doesn ́t elevate my principal component score. Is this accepted? They do it in other instructions i ́ve seen 4. Having in mind that doing a PCA analysis is a iterative process, how do i know when i have the best possible result? 5. Are there still advantages to doing both PCA and a Factor analysis and comparing the results?
Mehma
Dear Mehma,
1) the amount of total variance explained should be higher or at least equal to 50% for a reasonable PCA analysis;
2) your criteria make sense only if you can justify them with previous validated pertinent literature;
3) rotation is very important in order to maximize the effectivenss of your factor analysis, so I suggest you to conduct a varimax rotation and see if this improves your PCA extraction results;
4) EFA/PCA allow you to find the latent factor/variable associated to a set of observed variables (items); you'll have a satisfactory factor analysis if the factor loadings of your items are high enough (>0.50), and this is confirmed by adequate levels of CR (composite reliability), AVE (average variance extracted), and Cronbach's alpha values of your "scale" (i.e., the set of items forming your latent variable). Hence, you should delete the items showing low factor loadings; try to do so and see what happens to the aforementioned validity indicators of your scales.
5) PCA is a type of EFA aimed at reducing the dimension of your dataset by aggregating items in latent variables; next, you should validate these explorative steps with a CFA (confirmative factor analysis) assessing fitting indexes of your construct (relative chi-square, GFI, RMSEA, CFI, TLI, etc.).
Hope this help,
Best luck with your study!
Thank you for taking time to answer all of this, Lamberto!
This was easy to understand, and really helpful!
- Mehma
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