A Priori Power Analysis across levels of Measurement Invariance

[Michael Brienzo]

Hello,

I am working on my dissertation. My project is testing the measurement invariance of a scale across three groups. I was advised by a member of my committee to conduct an a priori power analysis for my baseline confirmatory factor analysis model, as well as for each level of invariance testing. 

My model specifications are:

• 6 factors
• 32 items
• 15 factor intercorrelations
• Free estimation of the first item of each factor (e.g., NA*x1)
• df = 449 (for three groups, df = 1347)
• N = 35 (for three groups, N = 105)

For subsequent models:

• Fixed estimation of the first item of each factor
• Specify the number of groups = 3
• Set equality constraints per level of invariance (loadings; loadings, intercepts; loadings, intercepts, residuals)

The issue I am having is that the sample size calculations for each invariance level seem too low. I do not have a lot of experience with measurement invariance, but my sample sizes (which should be estimated as the total sample size needed across the three groups) are:

• Configural: N = 10
• Metric: N = 11
• Scalar: N = 10
• Residual: N = 11

I have been using both lavaan and semPower2 and realize that this may not be the appropriate forum for this, but any assistance in troubleshooting my code is greatly appreciated.

Sincerely,

Michael

[Ingo Man]

I'll throw a few ideas out there. After looking at your example syntax, I briefly played around with the power specification in line 203 [configural <- semPower.aPriori(effect = c(.08, .095), effect.measure = ‘RMSEA’, alpha = .05, power = .90, df = c(1347, 1365))]. When I enter “power = .10” there, it still returns n = 10. Maybe something is missing in the syntax?

So far, I’ve only worked with Monte Carlo simulations, using the great tool by Wang and Rhemtulla:

Wang, Y. Andre, and Mijke Rhemtulla. 2021. “Power Analysis for Parameter Estimation in Structural Equation Modeling: A Discussion and Tutorial.” Advances in Methods and Practices in Psychological Science 4 (1): 2515245920918253. https://doi.org/10.1177/2515245920918253

This allows the power to be calculated separately for each parameter.
local power (power of determining specific effects within the model). See also here: https://jihongzhang.org/posts/2022-04-29-power-analysis-for-sem/
This has worked best for me so far.

Best regards, Marcus