Citing Claims

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I find that there are specific claims in SEM research that float around, but where they come from is often forgotten. So, I've made a list of these claims with some quotes and explanations below. Of course, I have also included a citation if the claim can be substantiated. If you have heard of a claim and know its source, feel free to email me and I'll determine if it should be added here. If you would like to cite this page in addition to the sources provided below, here is the recommended citation:


Four Indicators Per Factor

Claim

Have you heard the one about the "optimal number of indicators" per factor? I have heard it a few times, and I know I have read it in multiple places. I include one of those sources below.

Source

  • Hair, J. F., Jr., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Upper Saddle River, NJ: Prentice Hall.

On page 678:

"In summary, when specifying the number of indicators per construct, the following is recommended:

  • Use four indicators whenever possible.
  • Having three indicators per construct is acceptable, particularly when other constructs have more than three.
  • Constructs with fewer than three indicators should be avoided."

Rationale

Joe's logic is that a minimum of three indicators are needed for identification, but four is a safer and more reliable configuration. More than four may result in a failure of unidimensionality (i.e., there may be multiple dimensions being captured). He also suggests four is the optimal number of indicators because it balances parsimony (simplest solution) with requisite reliability (all-else-equal: reliability increases as number of indicators increases).

Covarying Error Terms

Claim

Some claim you can covary error terms in a measurement model (CFA) under certain conditions in order to improve model fit. Others say you should always avoid it. In the past, I have taken both stances, with logic to support my decisions. However, as I've grown in understanding of SEM, I am more inclined to avoid covarying error terms if at all possible.

Source

  • Hair, J. F., Jr., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Upper Saddle River, NJ: Prentice Hall.

On page 675:

"You also should not run CFA models that include covariances between error terms... Allowing these paths to be estimated (freeing them) will reduce the chi-square, but at the same time seriously question the construct validity of the construct."

Rationale

Including a covariance arrow between errors implies that there is some relationship between the items of these variables that you are not accounting for properly in your model. Allowing their errors to covary essentially ignores the problem, much like putting a light bandage over a bullet wound without removing the bullet. It covers up the issue on the surface, but does nothing to address the underlying concerns.

More to come

Claim

Source

Rationale