I am running an Exploratory Factor Analysis (EFA) for a variable.
EFA showed that the first six initial eigenvalues were more than 1, so I needed to retain them according to Larsen & Warne (2010) and Shrestha (2021) stated that researchers retain all factors for which the eigenvalue is greater than 1.0 following the rule of Guttman (1954).
The seventh component was also 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.
Therefore, I have been trying to find a reference to justify my action. Please provide me with references that mention that an initial eigenvalue less than 1.2 is typically considered insignificant and may justify removing a factor.
Thank you.
The decision to remove factors or components based on their initial eigenvalues in factor analysis or principal component analysis (PCA) is a matter of judgment and should be justified based on the specific context of the research and the characteristics of the dataset. While there are guidelines and rules of thumb for determining the number of factors or components to retain based on eigenvalues, there isn't a universal cutoff value that applies in all cases.
However, if you're considering removing factors with initial eigenvalues larger than 1 but less than 1.2, you would need to provide a rationale for doing so. Here are a few potential justifications; for example, substantial reduction in variability, Theoretical Justification, cross validation, etc.
You can look into the following sources:
1. Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate Data Analysis (8th ed.). Cengage.
2. Gorsuch, R. L. (1983). Factor Analysis (2nd ed.). Lawrence Erlbaum Associates.
3. Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.
Dr Amit Kumar,
Thanks a lot for replying
I have run EFA for one construct, which contains six sub-constructs; therefore, the first six factors were suitable according to the research's specific context and the dataset's characteristics. Thus, the seventh factor, which is between 1 and 1.2, is unnecessary to retain. Is that enough to justify?
This is my justification based on the results below:
Although the 7th component's initial eigenvalues are 1.127, which is greater than 1:-
(1) 8.529
(2) 3.115
(3) 2.559
(4) 1.933
(5) 1.748
(6) 1.427
(7) 1.127
(8) 0.970
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So, factors with eigenvalues below 1.2 might not substantially explain the variance in the data (Shrestha, 2021). Therefore, the seventh component is considered less important to retain. Component (8) is already below 1, so there is no need to retain it.
What do you think, Dr.?
Source: Shrestha, N. (2021). Factor analysis as a tool for survey analysis. American Journal of Applied Mathematics and Statistics, 9(1), 4-11.
Yes, you are correct!
Consider whether the inclusion of the seventh factor aligns with the theoretical framework of your research. If the first six factors adequately represent the constructs you're interested in, and the seventh factor does not contribute substantially to the understanding of the phenomenon under study (as you said), it may be justifiable to exclude it.
Eigenvalues represent the amount of variance explained by each factor. Generally, factors with eigenvalues greater than 1 are considered for retention. However, if the eigenvalue of the seventh factor is close to 1 and substantially lower than those of the first six factors, it suggests that the seventh factor accounts for relatively little variance and may not be essential for interpretation (it is visible in your results).