Summed Raw Scores as Latent Variables PreviousNext
Mplus Discussion > Confirmatory Factor Analysis >
 Nidhi Kohli posted on Wednesday, September 07, 2011 - 12:10 pm
I have 3 instruments:

1) Real Relationship Inventory (RRI-C) which is a 24-item measure designed to assess two dimensions of the therapeutic relationship: realism and genuineness. The internal consistency for the RRI-C as measured by Chronbach’s alpha was .90 for the Realism subscale, and .91 for the Genuineness subscale.
2) Working Alliance Inventory – Short Form (WAI-S) to assess the nature of the relationship between the therapist and the client from the client’s perspective. The WAI-S is a 12-item inventory that explores the three specific components of the overall dimension: Task, Bond, and Goal. The internal consistency as measured by Chronbach’s alpha is .93 on the overall alliance dimension.
3) Counselor Rating Form - Short (CRF-S), a 12-item measure with each item composed of an adjective describing counselor characteristics across three dimensions with each dimension rated on a 7-point Likert scale. The three dimensions are expertness, attractiveness, and trustworthiness; internal consistency reliability coefficients for the three dimensions are .90, .91, and .87, respectively.

My question is: Does the summed raw scores on the total scale or sub-scale for each of the instrument described above can be treated as latent variables? In other words, are summed raw scores similar to latent variables in this context.

Thank You.
 Bengt O. Muthen posted on Wednesday, September 07, 2011 - 5:00 pm
If you sum enough items that you know are reliable and unidimensional, working with your summed score is going to be close to working with a latent variable. But you don't know about the dimensionality until you have done factor analysis. Cronbach's alpha is known to not be of sufficient help in this. You may want to post your question on a more general discussion board like SEMNET.
 Nidhi Kohli posted on Thursday, September 08, 2011 - 8:58 am
Thank you very much for your quick response. Your explanation makes sense to me.
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