I want to test a model in which all possible paths between variables are captured (see fig 1) and then upon reviewing the path coefficients, remove non-significant paths (fig 2). Obviously with fig 1 this is just-identified, thus model fit cannot be assessed. However, once the non-sig paths are removed, the model is overidentified. Would it be acceptable for me then to assess model fit?
This is a classic approach to SEM, where you want to compare the chi-sq values from the two models to determine whether there is a significant decrease in fit.
Hello Lisa,
People do, in fact, follow that process. However, since it is an opportunistic method (e.g., look at results, modify model; repeat), it is quite possible that the solution might be idiosyncratic to your data set. Hence, replication (with additional data) is strongly recommended to validate the modified model.
Good luck with your work.
If you have a large enough sample, you can do an internal replication by dividing the data in half. That way, you develop the model in one half and test it in the other.
I would recommend reading the book of structural equations of Gana and Broc (2019)
David L Morgan, thank you for taking the time to answer. I would like to compare the chi-sq values however if the first model is just-identified my impression is that it wouldn't make sense to compare the chi-sq value of the second model (which would theoretically hope to show better fit) to the first model (which would have perfect fit due to saturation), is that right?
You test the difference in chi-sq values using the difference in Dof, which in this case would be the number of paths that you set of zero. Of course, that modified model will not fit as well as the fully saturated model, but the question is whether the difference is significant
David L Morgan excellent yes that makes sense - Thank you for your help
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