As far as I understand You have built second ordered model if You parcelled items (such models have smaller number of degree of freedom in opposition to hierarchical models). If each latent variable has 4 to 6 parcels model is at least identified. So far so good. I have never heard sensible explanation why latent variables should have the same number of obseved variables. According to my experience latent variables can have different number of observed vaiables.

As far as I understand You have built second ordered model if You parcelled items (such models have smaller number of degree of freedom in opposition to hierarchical models). If each latent variable has 4 to 6 parcels model is at least identified. So far so good. I have never heard sensible explanation why latent variables should have the same number of obseved variables. According to my experience latent variables can have different number of observed vaiables.

As far as I understand You have built second ordered model if You parcelled items (such models have smaller number of degree of freedom in opposition to hierarchical models). If each latent variable has 4 to 6 parcels model is at least identified. So far so good. I have never heard sensible explanation why latent variables should have the same number of obseved variables. According to my experience latent variables can have different number of observed vaiables.

Oserved variables can come from different techniques. What is important is than within latent variable thay must measure the same feature. 

I believe you choose factorial algorithm as one of the parceling method in your analysis. No, you can create the parcell in different amount of the parcel indicator. You can read thesis entitled " Use of item parceling instructural equation modeling with missing data" by Fatih orcan 2013

Hi Melissa,

I know that is not really the answer to you question, but a better and easier option would be to avoid parceling altogether and use the very best and focused raw indicators for your latent variable. When you use parcels, you assume but not test the the homogeneity of the parcels. If the parcels are multidimensional, the latent variable has no meaning at all and, hence, the structural model, too. The "domain-representative" approach in particular clearly violates the essence of the factor model (i.e., the latent variable causing a bunch of indicators). 

Begin by considering what the latent variable really should mean and then select those indicators that most perfectly reflects such an entity. Then test the model and learn from possible model misfit.

HTH

Holger 

There are some limitations with item parcels. This might be a good guide 

http://www4.ncsu.edu/~awmeade/Links/Papers/Parceling(SIOP05).pdf

Thanks Agnieszka for the prompt answers!

Thanks Wan Mohamad for the reading recommendation!

Thanks Dr Steinmetz for your caution and suggestions. Perhaps I should clarify that I'm running covariance-based SEM, and my research is not so much concerned about the indicators and their latent factors than the relationship between latent factors. The reason I'm using parcels is to restore the unidimensionality of my latent factors that were measured using multidimensional scales, since I am interested in the factors as unidimensional ones. I hope I'm making sense. I referred to: 

Todd D. Little, William A. Cunningham, Golan Shahar, and Keith F. Widaman. (2002). To Parcel or Not to Parcel: Exploring the Question, Weighing the Merits. Structural Equation Modeling, 9(2), 151–173. 

Also, since my analysis is confirmatory rather than exploratory in nature, I reckoned that it would not be desirable for me to remove 'weak' raw indicators and only retain the best ones (my faculty members certainly do not like that). So parcelling was the way to go for me. Would you think that this is inappropriate? Your input is highly appreciated. 

Thanks Dr Paxton, I should add that when I ran CFA for each variable, I used raw indicators but in the final full-fledge model, I used parcels as indicators.

Dear Melissa, as I wrote, if the measurement model is misspecified, the latents are unreasonable and, hence, the structural model is deeply flawed. You can not separate both parts of the model.

Latents or factors (as special latents) are ALWAYS unidimensional (by definition) - the question is: Does a latent has the supposed theoretical meaning or (a) a different meaning, or (b) no meaning at all (i.e., is an artefact). This is the most essential part of any analysis. 

In your last reponse to Raheem Paxton, you said that you did already CFAs with the indicators. Why separate both analyses and not go for an integrative model including all indicators? 

Just my 2 c 

Holger

Dear Dr Steinmetz, you're right to say that both analyses should not be separated - this reminds me to be mindful of how I report my results.

Yes I started out doing CFAs with indicators, then I ran CFAs with the parcels to ensure that the measurement models with parcels fit the data as well. I then used parcels in the integrative model mainly because of model parsimony. Does it really matter whether the parcels are homogeneous if I have done both of these CFAs?

Is it right to say that the CFAs with indicators would have answered the question of whether the latents are valid/ measuring the intended meaning? 

Also, if my measure has subscales, does that not indicate that the measure is multidimensional in nature, and therefore one of the ways to restore the unidimensionality of the latent is to use parcelling? 

I'm really no expert in SEM so I thank you in advance for your valuable input!

Hi Melissa, testing the CFA in a first step is at least a good thing (most of parcel users don't do that). It is rather a question of the logic of the whole analysis. If I were the reviewer I would question why you separated both steps when both steps could be integrated in one full model. 

IF the CFA were fitting THEN parceling would be reasonable. But again: why parceling, when the raw-indicator model worked? There may be some statistical reasons (e.g., parcels are closer to the continous data requirment than indicators) but this can be circumvented by using the appropriate estimators (e.g., WLSMV, DWLS or robust estimators such as the Satorra-Bentler-corrected chisquare).

A SEM as I understand it is an attempt to explain the observed world. The indicators are (response) behaviors - and thus, part of this world. When you create parcels you move away from this world as you compute something by yourself. I don't like that but that depends on the personal perspective on SEM.

And finally, yes, subscales imply multi-dimensionality. Don't think in terms of scales or constructs - think in terms of unobserved causal entitites in form of variables (degree of something which exists) - these are latent variables. The latent variables IN MODELS should reflect these theoretical entities as close as possible. Then consider your observed world (the indicators) and consider a causal structure consisting of latent variables that you think is responsible for this observed world to get its form. This MAY be a common factor model (one latent variables causing a bunch of indicators) or some/all of the indicators measure different latent variables which cause each other. That is, the factor model is ONE option.

Here are some non-mainstream but enlightening articles that should help:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4297459/pdf/12874_2014_Article_1153.pdf

http://www.biomedcentral.com/content/pdf/1471-2288-12-159.pdf

http://www.sociology.ualberta.ca/FacultyStaffandGraduateStudent/AcademicStaff/~/media/Sociology/Documents/Docs-G-K/FittingFactorModels_(1).pdf

Best,

Holger

Hi Dr Steinmetz, thanks again for your clear explanation. I should say that two of my latent variables had raw-indicator CFA models that were a good fit but the other two were not well-fitted. I'm using the ML estimator and hence my models are factor models with no cross-loading of indicators. I will read up on other estimators and check out those articles you shared too.

My sincere thanks for your guidance, Dr Steinmetz. Have a great day! 

Great discussion beyween Melissa and Dr. Steinmetz. Cleared so many confusions.