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I have a resilience scale with 11 items (observed variables), from which I calculated the mean to get a "resilience score" (what would usually be an unobserved variable or latent construct in SEM terminology).

  • Can I just use this resilience score to build a SEM in AMOS or do I need to include the 11 items as well ?
  • If I just included the resilience score as an observed variable, would it be considered a limitation or would it be all wrong?
  • In general, Is it valid to include a composite variable in a structural equation model in AMOS when such variables are treated as observed variables?
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2 Answers

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In general, structural equation modelling (SEM) with all observed variables is typically called path analysis.

One of the main motivations for SEM is to attempt to model relationships between latent variables. By including items rather than the composite score and modelling items as indicators of a latent variable you are able to assess relationships between latent variables.

In particular, with items rather than the composite score

  • you can assess your measurement model
  • you can get an estimate of relationships between latent variables (i.e., adjusting for measurement error).

Various middle grounds also exist including:

  • item parcelling: i.e., you create two or more parcels of items from your 11 items, and include these parcels as observed variables for a latent variable.
  • incorporate error of measurement into the model with observed variables.

It is not "invalid" to include a composite variable in SEM. However, it is in some sense invalid to say that inferences based on the observed composite variable are representative of the relationship between theorised latent variables. Most of the time, you'd want to adopt one of the other approaches (i.e., including items, including item parcels, or include measurement error).

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Thanks Jeromy!! I ended up here thanks to your blogspot! One doubt I still have (sorry I'm new with this!): I've read item parcelling can be criticized for not using the original items. Is this something that usually happens? The problem is -as I read- model fit decreases the more variables and the more items you have... That's why I was wondering if I could just work with composite variables – JuanD Aug 24 '12 at 23:45
Every case I've ever seen has poorer fit when you use all items than when you use fewer items or you use item parcelling. However, it is wrong to conclude that you should therefore not use individual items. Researchers should not blindly apply the same rules of thumb (e.g., rolling out the Hu and Bentler citation) for reasonable fit to models of very different complexity. – Jeromy Anglim Aug 25 '12 at 7:05
If you are going to model data at the item level, you may find that your measurement model needs to be adapted to get good fit (e.g., some items may have correlated residuals, some items may cross-load, etc.). That said, item parcelling tends can reduce the focus on the measurement model and increase the focus on the structural model. This might be good if you are having parameter estimation issues, or you just aren't as concerned about the item level issues. – Jeromy Anglim Aug 25 '12 at 7:09
up vote 1 down vote

If this is truly a scale, and the 11 observed items are endogenous, then your score contains a measurement error, and putting it into a regression model leads to biases: your estimates will be shrunk towards zero (see http://www.citeulike.org/user/ctacmo/article/2663962). This is a poor man's strategy for somebody who has SPSS, but does not have AMOS. If you have AMOS, there is little excuse in putting together a model that uses composite scores, rather than a full SEM that incorporates the measurement model for these 11 items. Besides improvements in accuracy of the estimates, you will also get the overall fit test that would allow you to judge how well your model fits the data.

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Thanks for your answer StasK!! As I said to Jeromy, the problem is that -according to my initial readings on SEM- model fit decreases the more variables and the more items you have. In this case I have resilience and 4 or 5 aditional latent variables (with its corresponding observed items). And here my model fit is hard to achieve. Would you recommend item parcelling as well? – JuanD Aug 24 '12 at 23:55
If you are trying to circumvent the goodness of fit test, you can do whatever you like. But you'd be cheating on yourself. – StasK Aug 25 '12 at 19:29

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