Whether sample size as 2000, which was derived with mathematical formula from the population is enough or less or more for the advance statistical analysis in terms of EFA and Structural Equation Model ?
I presume you mean Exploratory Factor Analysis. It’s not always too easy to answer, but I think http://pareonline.net/pdf/v10n7.pdf gives a reasonable picture. Ideally , of course, the more data you have to input to any method, the more information you should get out, without some arbitrary sample size rejection point. Therefore, I prefer a different worldview of what I think is ultimately the same kind of problem and mission: http://www.ncbi.nlm.nih.gov/pubmed/15822921 (Zeta Theory, essentially a high dimensional data mining perspective).
This sample size usually is enough for almost all analysis. For EFA you should be careful with the number of items your test has. Usually, for a stable EFA is recommended more than 10 subjects per item.
Regarding Structural Equation Modeling (SEM) it will depends on the type, number of factors, groups, items and estimator. Further, there are some fit index, for example CFI, that are sample dependable. If you have large sample these fit index will be overestimated, so you will need other index that are not sample related to make an unbiased decision.
Now, some psychometricians recommended that you can not use the same sample for EFA and SEM or CFA. You should divide your sample in subsamples and separately run the analysis. In that case, you should see if you sample is large enough to split for both analysis.
There are several articles and books explain how to proceed with this analysis systematically.
Thank you Fernandes ,
Please, can you attach some articles regarding large sample size (with the purpose of SEM AND EFA?)
Dear Lanka,
Here you will find some links for articles about EFA and SEM. Three of them are regarding SEM. For EFA you might check Andy FIeld's book. You can look up articles that strictly discuss sample sizes. However, they usually are heavily mathematical (I don't know what is your field). I think this articles might be enough to give an idea of what happens with very large sample, especially with SEM fit index. One article will give you an overview of the sample sizes used for EFA.
http://pareonline.net/pdf/v10n7.pdf
http://www.sciencedirect.com/science/article/pii/S0191886906003837
http://www.tandfonline.com/doi/abs/10.3200/JOER.99.6.323-338#.VL4fFvmIBcY
http://www.ncbi.nlm.nih.gov/pubmed/17716081
Best,
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