We measured three aspects (i.e. variables) of self-regulation. We have 2 groups and our sample size is ~30 in each group. We anticipate that three variables will each contribute unique variance to a self-regulation composite. How do we compare if there are group differences in the structure/weighting of the composite? What analysis should be conducted?
ChatGPT says:
To compare if there are group differences in the structure or weighting of the self-regulation composite with three variables, you can use a multivariate analysis of covariance (MANCOVA). MANCOVA is an extension of analysis of covariance (ANCOVA) that allows you to examine group differences on multiple dependent variables while statistically controlling for the effects of one or more covariates.
Here are the general steps for conducting a MANCOVA:
Remember to consult with a statistician or someone with expertise in statistical analysis if you are not familiar with the assumptions and procedures involved in MANCOVA. Additionally, ensure that your sample size is adequate for the analysis, as MANCOVA can be sensitive to violations of assumptions, especially with smaller sample sizes.
Are you thinking of self-regulation as a latent variable with the 3 "aspects" as manifest indicators? If so, you could use a two-group SEM, although your sample size is a bit small.
You've not said what software you use, but this part of the Stata documentation might help you get the general idea anyway.
https://www.stata.com/manuals/semintro6.pdf
Difficult to give a precise answer without more details on the exact experimental design and model, but first question would be: why use a composite and not the three aspects separately? Much easier to analyze, to interpret, not prone to compensations between aspects that may cancel any effect on the composite and so on…
Of course, beware of the multiple testing issue in this case.
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