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I need some advice to decide which aggregation method is better in my case. I want to create an aggregated variable which is a composite of 16 variables. All 16 variables are part of one big concept, so I think I could use PCA or CFA for this task. I need only one variable and not 16, since I will use it later as an independent variable in the regression analysis. My Cronbach's alpha is near 0.87 which is very good; however, since I have 16 items, it is not very reliable.

So first, I decided to use PCA, because I have a task of dimension reduction. However, a cumulative variance of the first factor is 0.55 and eigenvalues are low. I use predicted factor score in my regression and did not get the significant results. Then, I tried the factor , pf command from STATA and got much higher cumulative variance, 0.85, and eigenvalue for the first factor is above 8 (other methods like ML, PCF did not give me good results). I can also predict factor scores using this command. I am not sure, however, if I can use the command for EFA ( factor , pf as far as I understand is only for EFA, and for CFA I have to use SEM) to do CFA, and whether CFA is appropriate in this case.

My second question: are there some measures of goodness that could help me to choose between methods?

The last question is about $z$ scores: My 16 variables come from text mining and they are word counts that describe special topics, which could be aggregated to the bigger supertopic. Do I need to generate $z$ scores before doing PCA/CFA here? All variables are measured in the same way.

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    $\begingroup$ Factor analysis cannot account for more of the total variance than PCA can. So that you say EFA gives you higher percentage could be due to it giving you percent of the common, not total, variance, perhaps. $\endgroup$ – ttnphns Aug 3 '19 at 6:41
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The last question is about $z$ scores: My 16 variables come from text mining and they are word counts that describe special topics, which could be aggregated to the bigger supertopic. Do I need to generate $z$ scores before doing PCA/CFA here? All variables are measured in the same way.

You might want to check your software's PCA specifics, but I believe they are generally covariance based. If your variables have very different variances this may give the variables with higher variances an unintentional higher "weight" when calculating the component loadings. Calculating z-scores before conducting PCA will standardize that variances to ensure that each variable is weighted equally.

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  • $\begingroup$ Thank you for your answer, I also read that it is more appropriate to use z scores before doing PCA. $\endgroup$ – In777 Jan 4 '17 at 16:20

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