Principal Component Analysis - Optimal number of retained factors

[Fae]

I am trying to do dimension reduction using Principal Component Analysis.  The dataset have 25 variables and 300K obs. The data is for segmentation using 2-stage clustering (K-means clustering then Linkage clustering)

What's the good practices for deciding the number retained factors. Is criteria #1 good enough?

Criteria #1:  eigenvalue>1 

->  5 Factors with 54% variation explained.  Is the variation explained too low?  Should i use eigenvalue>0.7 and 

Criteria #2:  eigenvalue>0.7 and Variation explained > 0.7

-> 10 Factors with 78% Variation explained 

ods graphics on;

proc factor data=myData preplot plots=(scree initloadings preloadings loadings) method=principal rotate=varimax 
scree score;
var _numeric_

run;
ods graphics off;

#	Eigenvalue	Difference	Proportion	Cumulative
1	4.59175884	3.04985582	0.2551	0.2551
2	1.54190302	0.12646714	0.0857	0.3408
3	1.41543588	0.23647927	0.0786	0.4194
4	1.17895661	0.09521203	0.0655	0.4849
5	1.08374458	0.16097769	0.0602	0.5451
6	0.92276689	0.04595209	0.0513	0.5964
7	0.8768148	0.00522994	0.0487	0.6451
8	0.87158485	0.06006623	0.0484	0.6935
9	0.81151862	0.05330799	0.0451	0.7386
10	0.75821063	0.06929076	0.0421	0.7807
11	0.68891987	0.05741897	0.0383	0.819
12	0.6315009	0.02247774	0.0351	0.8541
13	0.60902316	0.01814238	0.0338	0.8879
14	0.59088079	0.03822865	0.0328	0.9207

[PaigeMiller · Accepted solution]

Honestly, I think the answer is totally subjective here. I don't believe that there is a universally accepted answer. The scree plot might indicate 7 factors.

However, I would say that if you (for example) choose the 5 factor solution, but find that factor 6 has a clear interpretation that makes sense in your application, that's a (again subjective) reason to include factor 6.

As far as the question about is 54% of the explained variability enough ... again there is no universal answer here, especially since every situation is different. For some data in some fields of application, 54% might be fantastic, while in other fields of application 54% might be poor.

[PGStats]

Useful advice is available here:

http://documentation.sas.com/?docsetId=statug&docsetTarget=statug_factor_details05.htm&docsetVersion...

[Daniel_Paul]

Hey,

an additional criteria would be the parallel analysis by Horn (1965; https://link.springer.com/article/10.1007%2FBF02289447). 

Bye, 

Daniel