Exploratory Factor Analysis Results: No significant loadings on last factors I am using MPlus 7.0 to run a factor analysis on a set of survey item data measuring positive traits.  I have used both oblique and orthogonal rotations and also have run it  as a bifactor model.  I ask for a 2 to 15 factor solution in each case.
The results always come back that the last half of the factors for any given factor solution yields loadings that are extremely low.  For example, if I look at a 7 factor solution, the last 4 factors will come back with very low loadings, so low that none of the items are even cross loading onto them (assuming >.32 loading criterion).  All the items load much more strongly on one or more of the first three.  This pattern persists if I look at the 3 factor solution: the last factor does not have any high loadings on it.
What could be causing this?
 A: You are likely attempting to extract too many factors from your item pool. If you have reason to believe that certain items should load to certain factors, then switch to a CFA approach. However, if you don't have a reasonable belief as to which items the factors should load, then stick with the CFA. How many factors to extract and what criteria to use is somewhat controversial. In the early 90s there were substantial discussions about this in reference to the EFA vs PCA debate. I can't find a clear consensus piece about what to do but instead do a bit of what all camps suggest. When I do a factor analysis, I use the following criteria:
1) Run the EFA.
2) Run Glorfeld's extension of Horn's Parallel Analysis and Velicer's Minimum Average Partials (MAP) test. See O'Connor's websitefor easy to use syntax. Examine the Scree Plot.
3) If I'm lucky, then all will be in agreement about the number of factors to use.
4) Examine the rotated solution to see if it makes sense (Personally, I always use oblique rotations because I'm doing exploratory analyses and it makes no sense to me to constrain the model to be orthogonal).
5) Re-run the model extracting 1 more factors. Examine the rotated solution.
6) Repeat 5 until the solution is clearly no good.
7) Aim to have a solution that makes conceptual sense and has at least 3-4 indicators per factor.
8) Extra factors where only 2 items load might indicate local dependence (check item wording/content).  
In my content area, this means I often end up with 2-3 factor solutions only.  
Hope this helps.
