I am running an exploratory factor analysis for six constructs. Each of them has eight items. The first six factors were more than 1, so I needed to retain them, but the seventh component was more than one but less than 1.2. How can I justify that the seventh component can be removed because an initial eigenvalue less than 1.2 is typically considered insignificant and may justify the removal of a factor? I have been trying to find a reference to justify my action. Please provide me the references that mentioned that an initial eigenvalue less than 1.2 is typically considered insignificant and may justify the removal of a factor.
I appreciate any help you can provide.
Factor selection criteria that are based on arbitrary eigenvalue cutoffs such as 1 or 1.2 are not very useful. There is little theoretical justification for a particular cutoff, and, oftentimes, these arbitrary cutoffs do not lead to meaningful factor solutions. Have you tried parallel analysis? See
Preacher, K. J., & MacCallum, R. C. (2003). Repairing Tom Swift's electric factor analysis machine. Understanding statistics: Statistical issues in psychology, education, and the social sciences, 2(1), 13-43.
https://kuscholarworks.ku.edu/bitstream/handle/1808/1492/preacher_maccallum_2003.pdf?sequence=1
Also, it sounds like you already have a theoretically expected number of factors (six), so why not use CFA (rather than EFA) in the first place?
To add to Christian Geiser answer: parallel analyses tend to overestimate the number of factors with increasing sample sizes, since the mean simulated eigenvalues will decrease with increasing N. Without further considerations, even the plausible parallel analysis may lead to wrong decisions.
Therefore, I would second Christians proposal to use CFA, if you already have a theoretical model.
One more vote for using Confirmatory rather than Exploratory Factor Analysis.
The eigenvalue represents the amount of variance each factor accounts for. Each extracted factor will have an eigenvalue (the integer multiple of the original vector). The first extracted factor is going to try to absorb as much of the variance as possible, so successive eigenvalues will be lower than the first. Eigenvalues over 1 are “stable.” The total of all eigenvalues is the number of observed variables in the model. Each variable contributes a variance of 1. Eigenvalues are then allocated to factors according to amount of variance explained.
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