I performed the single common method factor approach to diagnose a bias for my data. This test reveals that the fit indices of the model with latent common factor are very similar to those in my hypothesized measurement model. In addition, the Chi-square difference between the two models is not significant, what these findings mean?
If the Chi² significance test for differences is not significant the two models seem to fit equally good to the data. The problem with this test is that with a great sample size every difference becomes significant, but with a small sample size it becomes very conservative. You also checked fit indices (AIC and BIC I guess? they are used to compare models) and if they show the same effect (that the models are fitting nearly equally good) you can expect that there is no meaningful bias: The bias corrected model does not fit better than your original model.
If the Chi² significance test for differences is not significant the two models seem to fit equally good to the data. The problem with this test is that with a great sample size every difference becomes significant, but with a small sample size it becomes very conservative. You also checked fit indices (AIC and BIC I guess? they are used to compare models) and if they show the same effect (that the models are fitting nearly equally good) you can expect that there is no meaningful bias: The bias corrected model does not fit better than your original model.
Thank you very much about your answer but please can you appoint a specific reference for this answer.
I have to look it up, but I guess you can find something in Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics. Boston: Pearson. There is a chapter concerning structural equation modeling and the chi²-difference test.
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