Hello colleagues
I noticed that sometimes researchers runs confirmatory factor analysis at the sub-scale level with no items included for any sub-scale. Those researchers run the analysis by aggregating the CFA to the sub-scale level. For example, the CFA model includes Z as the main latent construct and X1, X2, and X3 are the three sub-scales. No items are included for any sub-scale. My questions:
1- Is this a good analysis strategy for the CFA model?
2 Why and When do researchers use such analysis strategy?
3. Any textbook or papers that discuss this issue?
Kind regards
This strategy would be appropriate if the subscales measure a single unidimensional construct. An advantage may be that the subscale scores already represent aggregates (e.g., sum scores across multiple items). As such, they may be closer to truly continuous (metrical) scores than individual items (the analysis of item-level/ordinal data can be somewhat more complicated in terms of estimation methods). Using aggregates (subscale scores) also simplifies the model (fewer indicators). If the sole purpose of the analysis is to account for measurement error and if it is known that all subscales reflect the same unidimensional construct, then such a strategy may be useful and appropriate.
On the other hand, I think that an item-level analysis (including all indicators at the subscale level) should be done first to examine the psychometric properties of the items within each subscale and across subscales. Also, one could ask the question of why there would be different subscales in the first place if they all measure the same construct. So there is no 100% clear-cut answer to your questions: "It depends."
Article Confirmatory factor analysis of the Evidence-Based Practice ...
Confirmatory factor analysis (CFA) is a statistical technique that is used to test the fit of a theoretical model to observed data. In a CFA model, a latent (unobserved) construct is measured by a set of observed variables or items. The latent construct is typically represented by a factor, and the observed variables are typically represented by items.
It is not uncommon for researchers to run a CFA at the sub-scale level with no items included for any sub-scale. In this case, the CFA model would include the latent construct (Z) and the sub-scales (X1, X2, and X3), but no items would be included for any of the sub-scales. Instead, the items would be aggregated to the sub-scale level, and the CFA model would fit the aggregated data.
There are a few reasons why researchers might choose to run a CFA in this way:
Overall, whether or not it is a good strategy to run a CFA at the sub-scale level with no items included for any sub-scale will depend on the specific research question being addressed and the data that are available. It may be helpful to consult with a statistician or a researcher with expertise in CFA to determine the best approach for your specific research question.
There are a number of textbooks and papers that discuss CFA and the use of aggregated data in CFA models. Some examples include:
- "Confirmatory Factor Analysis" by Rex B. Kline, published in the Handbook of Psychological Testing (2013)
- "Using Confirmatory Factor Analysis to Understand the Structure of Psychological Measures" by George A. Marcoulides and Rick H. Hoyle, published in the Journal of Educational and Behavioral Statistics (2008)
- "Confirmatory Factor Analysis: A Preface to LISREL" by J. Scott Long, published in The Sage Handbook of Regression Modeling (2002)
You may also be able to find additional resources by searching online or consulting with a statistician or researcher who has expertise in CFA.
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