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I am trying to teach myself how to do CFA on the fly, with no formal training in statistical analysis (my first grad course on quantitative analysis is next semester).

I believe that I have figured out how to run a CFA using lavaan in R, and I know what kinds of values I should be looking for with the fit indexes and such, but I am not sure how to interpret the results when most of the parameters look good and some are not.

In the following sample from my results, I have great CFI (0.995) and TLI (0.984) numbers; RMSEA (0.047) looks good; SRMR (0.015) looks great; but the p-value for my RMSEA is really big (0.482).

Does that large p-value invalidate the model? enter image description here

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A few considerations for your post/question:

  1. The p-value you reference corresponds to a test of "close fit", which in this case is operationalized as an RMSEA of .05 or smaller ("RMSEA <= .05"). Your p-value of .482 indicates that you cannot reject the null that the RMSEA is .05 or smaller, which is a good thing if you are hoping to retain this model.
  2. I realize that this wasn't something you had asked about, but you might want to consider the role of measurement (un)reliability in the appraisal of your model fit indexes. McNeish et al. (2018) provide a nice accessible review of this problem, whereby greater measurement reliability (in terms of standardized loading values) actually makes it more likely that you will reject a decent model according to the standard Hu & Bentler (1999) cutoffs, and more likely to retain a poor model with less measurement reliability. If your standardized loadings for the variables in this model are < .70-75 (the values specified in Hu & Bentler's simulations), their cutoffs may be too liberal for your model. Your model also appears to be barely over-identified (only 2 degrees of freedom), which means you don't have a ton of information to appraise the issue of model adequacy in the first place.

References

McNeish, D., An, J., & Hancock, G. R. (2018). The thorny relation between measurement quality and fit index cutoffs in latent variable models. Journal of personality assessment, 100(1), 43-52.

Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural equation modeling: a multidisciplinary journal, 6(1), 1-55.

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