Nested vs non-nested model?

Hi all,

I am running a confirmatory factor analysis and trying to work out if my two models are nested or not - this will be important for me to decide how I compare the models (e.g. using just the AIC and CFI statistics to compare the two models, or whether I can also use the chi-square difference test to compare the model).

Can anybody help me determine whether my models are nested?

My original model has four factors - each with 10 items.

My amended model has three factors, the first and second factors have the same 10 items aligned to them as before. The third factor has 20 items, taken from the third and fourth factors of the original model.

Would this be a nested or a non-nested model? Do we need more information? (e.g. a diagram from a SEM program?) I think it is not nested but want to be absolutely sure.

Take care



Cookie Scientist
So basically you collapsed the 3rd and 4th factors into a single factor. Right?

Yes, these are nested models. Model C is said to be nested in Model A if it is possible to constrain the values of certain parameters in Model A (for example, by setting certain correlations to 0 or 1) and thereby obtain a model that is equivalent to model C. In this case, we could take Model A, the 4 factor model, and constrain the correlation between the 3rd and 4th factors to be 1, and this would be equivalent to having Model C, the 3 factor model.
Hi Jake,

Thank you so much. The way you describe it has highlighted the logic I needed to understand (and now justify) that my models are nested.