I am stuck. I am developing a new scale and am currently carrying out EFA. The theoretical factors are 6, with 40 variables measuring it. My sample size is 214 (sample to item ratio of > 5:1). I need insights on the following:
1. While the KMO measure of sampling adequacy for the 40 variables is 0.946, for individual variables (as seen in the Anti-image matrix) is quite low (0.2 to 0.5). I have done PCA (varimax rotation). Bartlett’s Test is also highly significant. What should I do? Should I be concerned about this?
2. I get 6 components and have considered loadings above 0.4. I find few items quite similar and intuitively feel dropping few should be fine. I look at the inter-item correlations and find them ranging between 0.5 to 0.65. Are these high enough for me to drop? What else can I consider to drop items? Cross loading I am dropping...
Will deeply value insights.
Regards,
Vikas.
If the researcher is an expert on that subject (EFA and subject), you though deeply and decide...I will do an experiment with the results of exploratory factorial analysis results...the experiments to determine predictive utitlity of the scale (e.g. ROC curve, bayesian statistics like Youman index or S, Specificity, etc.) assigning scores accordingly the first loading or reproducibility items table, I hope it helps...good luck!!! Remember...EFA interpretation is for intuitive and creative researchers...You will solve it!!!
There is an old joke about exploratory factor analysis. A mathematician, a statistician, and a factor analyst walk into a bar. The bartender thinks about how academics are always making things too complicated and decides to have some fun. He says he will give free drinks for the night to the one who gives the best answer to the question, "How much is 2 + 2."
The mathematician says, "Well assuming we are using base 10 and non modular arithmetic 2+2=4."
The statistician says, "since all of your observations have error, and assuming those errors are uncorrelated and of equal size, 2+2 = 4 +/- 2 epsilon.
The factor analyst says, "What would you like it to be?"
Jokes aside, if you have developed a scale based on existing theory (and especially with only about 5 subjects per variable, I question the utility of EFA at all. A CFA approach, comparing your model to a single factor or other competing models, is likely to be more illuminating.
In addition, if your items are binary, EFA is likely to be complicated by spurious difficulty factors.
Finally, similar to the previous respondent, think about all of this in the context of the validity argument you would like to make. How does this analysis support the inferences you want to be able to make from the test scores?
With all that in mind, especially how the scores will be used, what does dropping the items do to your scale reliabilities? If you are making only group level inferences you are probably fine. If you are making individual level decisions, perhaps not.
Norman, many thanks for your insights. My creative buds are getting activated and I proceed with my analysis with renewed vigor.
Kingston, I am clear now...will proceed with the question on "what would I like it to be?" and I am sure to find the answer..:-) "Many a true word is oft spoken in jest" !!!. I thank you for al the point stated and am pondering over them.
Mutasem: Thank you. I have read this article.
Chalamalla: I would love to have this article; however, not able to get it. Do you have this article? Will appreciate if it can be shared.
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