# cluster analysis after factor analysis: do I need to use all factors for cluster analysis?

I have a 127-question survey with 6-level likert type answers. With EFA I have kept 56 items and got 8 factors. With CFA (on sample not used in EFA) I confirmed these factors. so far all good.

When I tried to do cluster analysis, with 8 all factors I did not get clear solution (I used SAS, and used the CCC and pseudo F and T statistics indicators to judge the number of clusters; ccc: Cubic Clustering Criterion).

When I used 7 factors, I got a clearly solution of 3 clusters. All three indicators (CCC, pseudo F and statistics) suggested cluster number of 3. And further analysis with 3 clusters looks very reasonable to us.

my question is: Do I must use all 8 factors from EFA/CFA to do cluster analysis?

If I must use all factors, what can I do if it does suggest a clear number of clusters? It seems there is no much to tune.

if I use 7 factors but not 8 factors from EFA, will this be a problem and reviewers may question on this?

• There are a number of very unclear points in your question. To mention just two: 1) have a 127-question survey... With EFA I have kept 56 items and got 8 factors What does that mean? Did you do EFA on 127? You kept 56 based on EFA - i.e. meaning that you are developing a questionnaire and selecting items for it? If so then did re-doing EFA on those 56 items confirmed well that 8-factor structure? You have not explained all that - what you were doing. Commented Jul 15, 2016 at 20:16
• Next thing, are you clustering cases (data points) or variables (the items) - also unclear (for me, I'm sorry for being stupid). Do I must use all 8 factors from EFA/CFA to do cluster analysis? What for? What is your purpose after all? Commented Jul 15, 2016 at 20:16
• I used 127 items in EFA and removed many based on communalities, low factor loading, cross loading, etc) and finally 56 left. I split data into two parts, one for EFA and the rest for CFA. And then I want to use cluster analysis to group cases (people, data points); purpose is to see difference between groups of cases Commented Jul 15, 2016 at 20:43

The quick answer is "no," you do not need to use all of the factors. More specifically, there is no "rule" or law about what you eventually use in creating a cluster solution. Moreover, each of the factors is an expression of all of the input variables.

Having done many cluster solutions over the years that were based on SAS Proc Fastclus, I found that there were three important input options:

• The "drift" option

• The "delete=" option setting a minimum floor to the size of the seeds

• Varying the number of input variables

If all the factors don't return a useful solution, then whack a few with the smallest eigenvalues and rerun it. Another useful idea is to put the first pass of Fastclus within a macro which loops from 3 to some appropriately large number of clusters, i.e., maxc=. Then, if a promising solution is found based on triangulating the CCC, the frequencies of the clusters and the inflection point for the pseudo-Rsquared, roll that out based on the original input variables.

• Thank you. I use proc aceclus followed by proc cluster with method=ward to get ccc, F and T statistics. But I found method=ward does not work for proc fastclus (syntax error if I use it in proc fastclus) Commented Jul 15, 2016 at 20:15
• I used to use Proc Cluster to curate the seeds for input into Fastclus until I figured out it was a waste of time. Not being a fan of hierarchical partitions, I never use Cluster, relying on Fastclus. Aceclus delivers elliptical solutions where Fastclus is spherical. Commented Jul 15, 2016 at 20:18
• do you mind sharing a little bit more on using Proc fastclus to determine the best number of clusters? In proc cluster using method=ward, SAS output 3 curves for CCC F and T^2 against number of clusters, which helps determine number of clusters. In Proc Fastclus it only generates one value for each, and how to use these to determine the best number of clusters? Thank you. Commented Jul 15, 2016 at 20:49
• Np. First, identify solutions with a spread in the frequencies across the clusters. Basically, this means avoiding solutions that put 40%-45% or more of the observations in one cluster. Next, within that set, identify the first solution that maximizes the CCC. If the CCC is always negative, either whack more input variables or take the least negative solution. Usually, maximizing the CCC will return something close to the inflection point for the pseudo-Rsquare. Commented Jul 15, 2016 at 20:54