# SEM: Comparing models when removing paths

I'm developing an SEM model for a study I've recently run. Essentially, I have 6 factors that are shown from previous research to predict one's performance in a specific task. My data is the composition of these factors from people and their performance scores on said task.

The challenge I'm facing is that there is some contradictory evidence that shows one of the factors does not contribute to the predictive value of one's performance, rather hinders it. In testing my hypothesized mode, I find the same results, where the factor in question is reducing the fit of the model, removing increases all fit indices of an SEM.

I am trying to find a way to test the statistical difference between these two models, but the only methods I can find are testing the differences between two models by adding paths (i.e., post hoc modifications).

Are there any methods currently available that tests the difference between tow SEM models when a path (manifest variable) is removed from the model completely?

I'm currently using Lavaan for this project.

Thanks!

The model with the factor is presumably nested within the model without the factor, so you can just perform a simple likelihood ratio test. Fit the model with the factor and the model without the factor, then use lavTestLRT to compare them. If the test is significant, there is evidence that the model with the factor fits better than the model without it.