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Define Same Conceptual Factors

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https://www.researchgate.net/post/How_can_I_clearly_define_factors_that_are_conceptually_the_same?pli=1&loginT=41lPzmLUjWZA5mqZPp1Tm8dihJJZB5kw7w6RfzpcnbILa_gL5DcSHID3p99d3tnPEiYUvv_np1uNW1KdZmw0yBXDU_aC&uid=qYOW8zyUx3zRaKQ7EQrjutc9j07C2EfauLy1&cp=re221_ft_j_e1_jp_p94&ch=reg&utm_medium=email&utm_source=researchgate&utm_campaign=re221&utm_term=re221_ft_j_e1_jp&utm_content=re221_ft_j_e1_jp_p94

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I am running an EFA on a data set with 250 observations. Factors 3 & 4 are basically the same conceptually (based on two questions: "Q12. Foods must be expensive to be of quality" & "Q17. I believe that expensive foods are good"). Standardization seems to be done properly. We also tried many different rotations. In most rotations, usually the factor based on Q17 has a small loading (usually around 0.5-0.6). Can we combine the two factors in EFA?

Also, our KMO is around 0.5. If I remove MSA values smaller than 0.5 it is significantly increased, but I have 2 factors (I was requested 4, not strictly, but I am afraid they are way too few).

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It sounds like you're facing some challenges in your exploratory factor analysis (EFA). Here are some suggestions:

Combining Factors 3 and 4: If Factors 3 and 4 are conceptually very similar and Factor 4 consistently has a small loading in different rotations, you may consider combining them into a single factor in your analysis. This can help simplify your model and make it more interpretable.

Low KMO Value: A KMO (Kaiser-Meyer-Olkin) value of around 0.5 suggests that your data might not be well-suited for factor analysis. You mentioned that removing items with MSA values smaller than 0.5 improves the KMO. This could be a valid approach to improve the factorability of your data, but keep in mind that it might reduce the number of factors you can extract.

Number of Factors: If you were initially aiming for 4 factors but your data doesn't support it, it's important to prioritize model fit and interpretability over a predetermined number of factors. You should select the number of factors that best represents your data based on various fit indices (e.g., scree plot, eigenvalues, explained variance) and the theoretical relevance of the factors.

Model Interpretation: It's crucial to ensure that the factors you extract make sense conceptually and align with your research objectives. If combining Factors 3 and 4 or reducing the number of factors results in a more interpretable solution, that might be a valid choice.

Consultation: Consider discussing your findings and challenges with a statistician or an expert in factor analysis. They can provide valuable insights and help you make informed decisions about your analysis.

Ultimately, the goal of EFA is to identify a factor structure that accurately represents your data and makes theoretical sense. Don't be overly rigid with the number of factors; prioritize the quality of your model and the interpretability of the results.

You did not mention what kind of extraction you used, but for combining questionnaire items into scales, the the most widely recommended techniques are either principal factors analysis or maximum likelihood, with oblique rotation (i.e., correlated factors). You also did not mention how many questions you asked or how you settled on a 4-factor solution.

Have you considered a Confirmatory Factor Analysis where you can test whether or not to combine your two single-item factors?

In summary, you can consider combining conceptually similar factors if they meet the criteria mentioned above. Additionally, improving the KMO value by removing items with low MSA values is a reasonable step, but ensure that you retain items that are theoretically relevant to your study. Finally, keep a balance between statistical rigor and theoretical relevance when interpreting your EFA results.

Q12. Foods must be expensive to be of quality

Q17. I believe that expensive foods are good

The first is the same as saying cheap foods do not have quality.

To break the ambiguity either edit Q17 to "I believe that (only) expensive foods are good" so they have the same meaning or change Q12 to "Expensive foods have quality."

The formulation of those two items should be revised if they are to measure the same thing.

@David L. Morgan pointed out that you

@David L. Morgan pointed out that you didn't indicate how you arrived at four as the number of factors to extract, rotate and interpret. The generally accepted way to do this is via parallel analysis. I supspect that parallel analysis would rule in favour of three factors.