Questions about measurement invariance, cfa, sem and latent growth.

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Morgan Casal Ribeiro

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Jun 9, 2020, 1:21:59 PM6/9/20
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Hello everyone.

I am trying to perform cfa, sem and latent growth modeling using lavaan and SemTools, but have a few questions. Although I have done a good bit of research, this is my first time using this methodology, so I’m sorry if anything I say is a bit confusing.

I would be really thankful if the group could confirm if my approach is correct:

  •  I have measured data for two different years, so first I tested my measurement model with a cfa (separately for each year, and for a combined dataset, all producing good fit).
  • Then I checked for measurement invariance between years, establishing configural, metric and scalar invariance, but residual invariance was not shown*. From what I understand, this is not a concern for my analysis.
  • I proceeded to structural equation modeling, and the structural model showed good fit to both years. For one of the years, the model showed good fit but none of the relationships between variables were significant (is that strange?).
  • I created a second-order latent growth model for each of my latent variables, to see if they changed significantly from one year to another, as well as to check if any sociodemographic variable I also measured influenced that change. One of the latent variables changed significantly from one year to another (both slope and intercept showed statistical significance) and was significantly related to a sociodemographic variable**.

Question 1: Does that process make sense, and are there any important steps that I may be missing?

*Question 2: Is the absence of residual invariance a problem for the rest of the methodology?

Question 3: After establishing measurement invariance for both years, is it valid to improve the measurement model of one of the years, adding a theoretically valid modification due to it having a high modification index and standardized expected parameter change, while keeping the model of the other year the same? (the change is adding something similar to “measured_variable1 ~~ measured_variable2”)

**Question 4: Do I also need to establish measurement invariance across the groups of the sociodemographic variable that was related to the latent variable change from one year to the other (latent growth model)? It is a numeric variable (household size, ranging from 1 to 10), but I have also divided it into groups (1-2, 3-4, 5-6, 7-8, 9-10) and the relationship with the latent variable change was still significant.


Sorry for the long post! If needed I can provide the data or the script, but it is a bit of a mess at the moment.
Thank you in advance!

Terrence Jorgensen

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Jun 12, 2020, 5:14:51 AM6/12/20
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SEMNET is a more appropriate forum, since this one is mainly for software support.


But briefly:

*Question 2: Is the absence of residual invariance a problem for the rest of the methodology?


No, since you are modeling growth among multiple-indicator constructs.  See first 2 articles:

 

Question 3: After establishing measurement invariance for both years, is it valid to improve the measurement model of one of the years


That would violate configural invariance.  I would recommend simultaneously testing the freeing of the same parameter at both occasions, after thinking carefully about which parameters you would consider it sensible to test such a hypothesis about.

 

**Question 4: Do I also need to establish measurement invariance across the groups of the sociodemographic variable that was related to the latent variable change from one year to the other (latent growth model)? It is a numeric variable (household size, ranging from 1 to 10), but I have also divided it into groups (1-2, 3-4, 5-6, 7-8, 9-10) and the relationship with the latent variable change was still significant.


Tests of its effect on the growth factors will assume invariance across the predictor.  You can use the MIMIC / RFA approach to test invariance without creating arbitrary groups.  Again, see top 2 articles (one is open access, the other is accessible on ResearchGate):


Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

Morgan Casal Ribeiro

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Jun 14, 2020, 10:09:37 AM6/14/20
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Thank you Professor Jorgensen! I will check out the other forum, but your advice has already been helpful :)
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