Two CFA vs second-order CFA

Hi All,

I'm working on my dissertation, and am evaluating the internal structure of a 34-item scale. The model in which the scale is based off of is hierarchical, and is structured/ordered as such: (1st) items, (2nd) item-groups, & (3rd) sub-scales. To evaluate this information I would use a structural equation modeling approach to confirmatory factor analysis.

I was debating on whether or not it would be better to construct two standard CFA models or one second-order/higher-order CFA model. In creating two CFA models, I would first include the scale items as the "measured variables" and the item-groups as the "latent variables." If there is adequate fit, I would then proceed to create the second model in which the item groups are the "measured variables" and the sub-scales are the "latent variables." Lastly, if I was to create a second-order CFA model, I would include (1st) items, (2nd) item-groups, and (3rd) sub-scales.

I would appreciate any insight, suggestions, or tips on what method is most appropriate for my goal.

Thank you all, very much!


Super Moderator
I don't have strong feelings one way or the other, but it might be a good idea to have a read about "item parceling" (item parcels are also sometimes called "testlets"). Whether or not to incorporate parcelling seems to be the main question here. One possibly useful article:

Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9(2), 151–173. doi:10.1207/S15328007SEM0902_1


Phineas Packard
I think a single higher order CFA is most appropriate. I am not a fan of two-step procedures as item groups, composte scores, or plausable values for latent factors tend to be biased. A HCFA is easy enough to fit and is a single step which does not lead to any unintentional bias.

In relation to CBs suggestions I dont think item parcels are what you are after a-priori. In addition, there will be a special issue in MBR in the coming months that suggests item parceling is not an appropriate solution as it tends to just sweep misfit under the rug (I am reading the proofs of the central article as we speak).

I am assuming here that you have a good reason to presuppose a hierachical measurement structure.....Is this a personality measure by any chance?
Thank you, both, for your responses. Lazar, I was doing some additional reading and it seems that the higher-order might be the better way to go... The measure I'm looking at pertains to career indecision. It includes ten topics which are then ordered under one of three categorical difficulties in the decision-making process.

CB, thank you for the article! Lazar, by any chance, do you have or suggest any literature that might provide more information on the matter?

Thanks, again!


Phineas Packard
Well that depends a little on what you are after. If you are looking at "how" to do it then I would get the Barbara Byrne book related to the SEM package you are using (EQS LISREL AMOS MPlus). If you are looking for examples I would guess the literature on academic self-concept has some of the best example as the hierachical nature of self-concept has been established since the late 70s. I would guess articles by Marsh or Yeung would provide some guidence. Here is a recent example of my work which uses HCFA