You may have as little as 2-indicators per construct, provided adequate identification constraints are imposed (equality of loadings, fixing mean/var to 0/1, etc.).

Regardless of your parcelling technique, you should have equivalent parcels across your 2 focal groups of interst (even if imperfect).

Hope this helps,

Matt

Hello William,

I can see where you are going on this. Usually a CFA for a SEM measurement model includes all factors with their indicators. There is no structural model and the factors are simply correlated to each other. This overcomes the issue of “needing” at least four indicators. Yes, you can run a CFA with only two items. You can even use a single item with modelled residual variance if the reliability (Cronbach alpha) is well accepted in literature. For myself, I find that factors with two items often throw up Heywood cases (problematic). I tend to use 3 items to ensure the factors are just identified, and usually require less constraints (as Matthew noted previously).

Once you have a “good” fitting CFA, you can move on to the structural part of the modelling.

To your second question, it is not advisable to confirm your measurement model (CFA) and then use different measurement items; you are not using the measurement model you confirmed. Furthermore, your next step beyond the measurement model for the complete dataset is to test measurement invariance between the control and experimental groups you are comparing. This is a critical step for your SEM analysis and involves ensuring that the latent constructs are understood by both groups in the same way (i.e., they mean the same thing b/w groups).

Chapter 9 & 16 in Kline’s book are good intros to CFA and measurement invariance, respectively. See: Kline, R. B. (2016). Principles and practice of structural equation modeling (Fourth ed.). New York: The Guilford Press.

Wishing you well in your research,

Tim

Hi Tim Edward Powers

Thank you for your response, if am I correct in interpreting your first paragraph correctly I should:

1: Run the SEM as a CFA with all latent factors in on model correlated, rather than having structural paths (rather than conducting a unique CFA for each latent construct, then combining them into a single SEM).

2: Establish the correct variance level

3: Move the SEM model by removing hypothesised correlations/including structural paths

4: Establish invariance level for the SEM

Hi William,

1. – Yes. This simply confirms your measurement of constructs used in your model are reliable, independent (in relation to the other factors in your model) and have an overall good fit. It may require some modifications with regards to the observed items, but you will need to defend these changes (e.g., similar wording, etc.).

4. – The next step, is to establish measurement invariance between both groups. See:

Van De Schoot, R., Lugtig, P., & Hox, J. (2012). A checklist for testing measurement invariance. European Journal of Developmental Psychology, 9(4), 486-492. doi:10.1080/17405629.2012.686740

Cheung, G., & Rensvold, R. (2002). Evaluating goodness-of-fit indexes for testing measurement invariance. Structural Equation Modeling, 9(2), 233-255.

Now you have simply verified the reliability of your measured factors, in relation to each other and across groups. Assuming they pass (i.e., CFA has good fit, and measurement invariance is established), you can now use the factors (with observed items in your measurement model) in your “structural” model and compare between the groups. These preliminary steps simply ensure your SEM latent constructs are trustworthy (assuming they are validated measures).

Keep in mind, you do not “have to” parcel down to two items. You may even decide to not parcel. However, you can run into problems of inflated Type I errors when fitting a model with many observed variables with a small sample (you did not mention your sample size). This is sometimes referred to as “model size effect”. So, parcelling may be appropriate. For model size effect, see:

Herzog, W., Boomsma, A., & Reinecke, S. (2007). The model-size effect on traditional and modified tests of covariance structures. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 361-390. doi:10.1080/10705510701301602

Shi, D., Lee, T., & Maydeu-Olivares, A. (2019). Understanding the model size effect on SEM fit indices. Educational and Psychological Measurement, 79(2), 310-334. doi:10.1177/0013164418783530

Hope this makes sense, William.

Tim