Should I do invariance test after my CFA model was created and model fits were good? Should I do common methods bias, too? If so, how do you do these procedures in AMOS?

  • $\begingroup$ @Aleksandr Blekh As you suggested, I have built a measurement model for my 4 factors measured by 25 items. The model fit' indicators are fine. Can I start to build structural model after this? $\endgroup$ – Ava XU May 6 '15 at 9:36
  • $\begingroup$ Note that 'how to do ____ in ____?' questions are off-topic here, so you may not get an answer to your request of AMOS help w/ an answer here. The other questions are certainly on-topic, though. $\endgroup$ – gung - Reinstate Monica May 6 '15 at 20:29
  • $\begingroup$ Nice question (+1); I'm glad you're moving forward. For some reason, my name's mention didn't work - I just saw your comment accidentally, when browsing questions. Please see my answer below. $\endgroup$ – Aleksandr Blekh May 7 '15 at 0:59

As far as I know, measurement invariance testing is usually performed in SEM context, when research sample contains multiple groups. In SEM context, measurement invariance is often referred to as factorial invariance. It is definitely a good idea to perform both measurement invariance analysis as well as common method bias analysis prior to creating structural models and this approach is actually recommended in the literature (i.e., Podsakoff, MacKenzie, Lee & Podsakoff, 2003; van de Schoot, Lugtig & Hox, 2012).

Gaskin (2012) provides excellent textual and video tutorials on performing CFA, including measurement model invariance testing and common method bias testing. While I don't have experience in performing CFA in AMOS (I prefer R), you are in luck :-), since many Gaskin's tutorials (and CFA ones, in particular) are focused on using AMOS. I highly recommend his materials, both textual and, especially, video. I hope that my answer is helpful.


Gaskin, J. (2012). Confirmatory factor analysis. Gaskination's StatWiki. Retrieved from http://statwiki.kolobkreations.com

Podsakoff, P. M., MacKenzie, S. B., Lee, J. Y., & Podsakoff, N. P. (2003). Common method biases in behavioral research: A critical review of the literature and recommended remedies. Journal of Applied Psychology, 88(5), p 879-903. doi:10.1037/0021-9010.88.5.879 Retrieved from http://isites.harvard.edu/fs/docs/icb.topic1392661.files/PodsakoffMacKenzieLeePodsakoff2003.pdf

van de Schoot, R., Lugtig, P., & Hox, J. (2012). A checklist for testing measurement invariance. European Journal of Developmental Psychology, 1(7). doi:10.1080/17405629.2012.686740 Retrieved from http://mplus.fss.uu.nl/files/2012/07/van-de-schoot-Lugt-Hox-2012-EJDP-Measurement-invariance.pdf

  • $\begingroup$ @ Aleksandr Blekh Thanks for your references. When you talked about multiple groups, you are talking about the different groups according different traits such as majors, age or sex? Am I right? If so, I will have many groups based on these different traits. How many groups should I do invariance test? My data were collected in a classroom settings. The traits I mentioned above were acquired through the demographic section of questionnaire. It is a multiple groups data? $\endgroup$ – Ava XU May 7 '15 at 2:48
  • $\begingroup$ @AvaXU: You're welcome. You understanding of multiple groups is correct. In regard to your other questions, I suggest you to watch this video tutorial (at least, first several minutes), which should clarify those issues for you. If there are too many groups, I guess, the optimal approach is to make assumptions about which groups' moderation effect might be more essential and perform invariance testing only for them. Alternatively and ideally, you should test invariance across all groups, existing in the sample. $\endgroup$ – Aleksandr Blekh May 7 '15 at 3:50
  • $\begingroup$ @ Aleksandr Blekh Thank you for all the knowledge you have shared! I will let you know how my research goes. :-) $\endgroup$ – Ava XU May 8 '15 at 1:15
  • $\begingroup$ @AvaXU: My pleasure! I look forward to hearing about your success. :-) $\endgroup$ – Aleksandr Blekh May 8 '15 at 3:30
  • $\begingroup$ @ Aleksandr Blekh I have set up my structural and measurement models. Could you help me take a look? If it is ok, please let me know. :-) My email is hengxu@d.umn.edu. THANKS. $\endgroup$ – Ava XU May 13 '15 at 5:30

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