Suppose a scale has 18 items on 5 points Likert scale and has no subscales. Is it necessary to do a CFA then?
It may be useful to conduct CFA if you wanted to test whether all 18 items really only measure one dimension (a single factor).
18 items are too many. it would not be easy to get good CFI and RMSEA scores. if you run CFA, you need at least N = 200 or N = 400.
if this scale is newly developed, you'd better run EFA to see the factor structure. if you find more than one factor (two or three factors). You may run a second-order CFA with two or three factors. Check some articles on a second-order CFA.
Again, with 18 items, it would be challenging to get good CFI and RMSEA for one factor model, but you may get reasonable results for a second-order CFA.
If a second-order CFA result good, you can still aggregate all 18 items to calculate one variable.
@Tae-Yeol Kim Thank you sir for the guidance, I have 400 sample size and the scale are old and well established so I guess I will go for CFA directly and I will look forward to understand 2nd order CFA
Hi, just two further comments regarding the second-order-proposal.
1) A second order factor reflects a specific causal model (not just an analytical convenience)--that is, the claim of the existence of a latent common factor that affects all primary factors.
2) A second order structure requires three outcomes to be just identified and deliver estimates. In this case however, it has no testable implications. That is, you can select together any three correlating factors and push a pseudo-second order factor onto it and you will not detect the error. You need at least four outcomes. These outcomes can be anything, the primar factors, other factors, or other manifest variables
3) There is a danger that you model noise (see the paper by Lee & Cadogan). Hence, you need some validity evidence for the second order factor (by incorporting other validation criteria).
Here is a link to a further discussion
https://www.researchgate.net/post/Scales_Subscales_in_Confirmatory_Factor_Analysis-how_do_you_analyse_them#view=5fd0852ede0d8552fe4a3716
Finally, with regard to the N-question: The sample size has two roles--to enable unbiased estimates (ML is biased in small samples) and for the model test.
IMHO the more relevant issue is the second one (as with a wrong model, estimates may be nonsensical ) and for that, you can apply the Swain-correction that corrects the chisquare test (and if you want the fit indexes), see for instance the R function contained in Herzog & Boomsma.
The N=200 rule is outdated (Boomsma & Hoogland, 2001) and tons of small-N misfitting model prove that the power to reject the (wrong) model was high enough :)
Best,
Holger
Boomsma, A., & Hoogland, J. J. (2001). The robustness of lisrel modeling revisited. In R. Cudeck, S. du Toit, & D. Sörbom (Eds.), (pp. 139-168). Scientific Software International.
Herzog, W., & Boomsma, A. (2009). Small-sample robust estimators of noncentrality-based and incremental model fit. Structural Equation Modeling, 16(1), 1-27. https://doi.org/10.1080/10705510802561279
Lee, N., & Cadogan, J. W. (2013). Problems with formative and higher-order reflective variables. Journal of Business Research, 66(2), 242-247. https://doi.org/10.1016/j.jbusres.2012.08.004
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