Hey everyone, I’m trying to set up a longitudinal Confirmatory Factor Analysis (CFA) model and I’m not sure about the best way to do it. I’ve got data from surveys done before and after a term, with 12 questions split into 3 latent variables (let’s call them A, B, and C).
Each variable has 4 questions tied to it. I want to compare the factor models between the pre and post surveys. I’m wondering if I should:
- Make separate models for each factor in pre and post surveys
- Create one big model with all factors for both time points
Here’s a rough idea of what I mean:
# Option 1: Separate models
model_A <- '
A_pre =~ Q1_pre + Q2_pre + Q3_pre + Q4_pre
A_post =~ Q1_post + Q2_post + Q3_post + Q4_post
'
# Option 2: Combined model
big_model <- '
A_pre =~ Q1_pre + Q2_pre + Q3_pre + Q4_pre
A_post =~ Q1_post + Q2_post + Q3_post + Q4_post
B_pre =~ Q5_pre + Q6_pre + Q7_pre + Q8_pre
B_post =~ Q5_post + Q6_post + Q7_post + Q8_post
C_pre =~ Q9_pre + Q10_pre + Q11_pre + Q12_pre
C_post =~ Q9_post + Q10_post + Q11_post + Q12_post
'
Which way is better? And are there any other things I should think about when setting this up?
Also, I was wondering if the equaltestMI package could be used for this kind of longitudinal CFA, or if it’s just for multi-group CFA. I’m not totally clear on the difference between these approaches.
Thanks for any help you can give!
Hey there ClimbingMountain! 
I totally get your confusion about setting up a longitudinal CFA model. It’s definitely not a straightforward process!
Have you considered using a hybrid approach? You could start with separate models for each factor to get a feel for how they behave individually, then move on to the combined model. This way, you’ll have a deeper understanding of each construct before diving into the more complex combined model.
One thing to keep in mind - make sure your sample size is large enough for the combined model. With 12 variables and multiple time points, it could get pretty parameter-heavy!
Oh, and about equaltestMI - it’s actually super useful for longitudinal CFA! You can treat your pre and post data as different ‘groups’ to test for measurement invariance over time. Cool, right?
Just curious - what’s the context of your study? Are you looking at changes in student attitudes or something similar? It’d be interesting to hear more about the practical implications of your analysis!
Keep us posted on how it goes, okay? This stuff can be tricky, but it’s also really fascinating once you get into it!
For your longitudinal CFA, I’d recommend the combined model approach. It provides a more comprehensive view of how your constructs evolve over time and allows for direct comparisons between pre and post measurements.
However, be mindful of potential issues with model identification and fit. You might need to consider adding constraints or correlations between error terms across time points.
Regarding equaltestMI, it’s actually quite useful for longitudinal CFA. You can treat your pre and post groups as if they were separate groups in a multi-group analysis. This allows you to test for measurement invariance across time, which is crucial for valid comparisons.
One additional consideration: look into autoregressive and cross-lagged effects between your factors. This can provide insights into how constructs influence each other over time, adding depth to your analysis.
hey mate, for longitudinal CFA I’d go with option 2—the combined model. it shows how factors behave over time. watch out for model complexity tho. measurement invariance tests work well, and equaltestmi isn’t just for multi-group analysis. goodluck!