Can I say a single variable with a high factor loading in an exploratory factor analysis is an additional factor? I'm doing a exploratory factor analysis for an investigator who wants to find factors from 7 variables. I did a preliminary analysis and found two main factors, each have 3 variables with loading > 0.6. There's one variable left alone for itself as a factor with loading >0.99. Should I report it as one factor or just leave it out and do another factor analysis? I heard a factor should include at least 3 variables.
 A: @Joe Question-1 : You can not consider a single variable/ question item as a factor. The factor  should have at least two variables / question items.  Question2 YOU may  undertake another EFA without this variable (however do justify). YOU have already done that and now you find factor -3 with var.2 + a few others as an alternative to erstwhile factor.  That is  the real purpose of EFA. Factor 3  (new one) is a valid factor as long as you can justify its contribution to dependant variable. Question 3 -  number of variables in a factor depends on accuracy of data , descriptive  or experimenta design etc. It is an issue that requires ingenuity and statistical acumen. best  wishes!
If you  can justify in theory that two factors are adequate to explain  the specified phenomenon, you can exclude  variable 3. The  third variable could be a confounding factor . And you can justify its exclusion saying that in net terms, there is no effect . Three or more " variables"  Ifor a factor  '  seems absurd  without evidence.
