Structural Equation Models - building with a large sample, and testing with a small one?

Question

I'm planning a study using Structural Equation Modelling to test different accounts of language learning. I would like to study a group of children with language difficulties. However, they are very hard to recruit and I'm aware that these models typically require at least 200 participants. One possibility would be

(1) Test SEMs on a large cohort of typically developing children - who are much easier to recruit (n = 500). (NB I'm imagining 3 or 4 different models each with about 3 or 4 latent variables).

(2) Apply these models to a smaller cohort of language impaired individuals (n = 80)

I'm imagining that in the second stage one would keep the coefficients from stage one, and would use some kind of procedure to manipulate the values of the latent (exogenous) variables to maximise model fit. Research questions would be

• Which model best describes the data for the typically developing children?
• Does this model also best describe the data for the language impaired children?

I'm wondering if this is statistically feasible and whether anyone has tried this approach before. Ta.

Answer 1

Re: The sample size issue. You are probably going to have a an issue with sample size. The more latent variables you have, and the more complexity you model, a larger sample is needed. However, I will also say that "rules of thumb" with these models is starting to go by the wayside. If you're that concerned why don't you just do a Monte Carlo study to justify your sample size. Check this article out for some guidelines. In addition, Bayesian Structural Equation Models show more stability with smaller samples, especially if you are willing to use informative priors. However, a misconception would be to assume any method is a "cure" for small samples. At 500, with a few latent variables in a simple CFA model, you are probably okay, but again run the Monte Carlo study and check yourself; however, 80 is very small.

Also, if the approach is to look at development within an SEM framework then you should read this book.

This leads me to the next series of questions:

• You use the phrase typically developing in your question. I'm a developmental scientist, so I can be a bit thorny about how the word development is used. You did not once mention modeling any kind of change process, so I'd be really careful how you talk about development. At the least, a cohort-sequential/accelerated longitudinal design would allow you to talk about development.
• It also sounds like you want to create a CFA model for the typically developing kids and see if it is invariant with the language impaired children, right? What's the hypothesis for how that's going to work out? I can't imagine many instances where the factor structure for typically developing vs. non-typically developing students would be the same, so I don't see how that would be really surprising, and I've dealt with language research for a large portion of my time in graduate school. However, I also don't know the specifics of your model. Something to think about...

Mixture models might be a cool angle when the sample size grows.

I hope that gets you thinking.