In the context of confirmatory factor analysis.
When building a CFA model, each of item that form a latent variable has its own squared multiple correlation coefficient or reability. Is there a minimum value for squared multiple correlations (R^2)? Could you please suggest some references?
Thanks & regards.
see
https://www.amazon.com/Applied-Linear-Statistical-Models-2013/dp/1259064743/ref=sr_1_1?keywords=applied+linear+statistical+models&qid=1567604916&s=books&sr=1-1
Best, D. Booth
Hello Nip Nip,
If you're asking, what should the minimal reliability for indicators of a latent variable, the answer depends on the use of the scores. For example, making decisions about individuals generally requires much higher reliability estimates (.90s) than making decisions about groups. In the context of CFA, here's a couple of potentially useful links:
1) https://eric.ed.gov/?id=ED395040
2) https://pdfs.semanticscholar.org/dbe2/03b16208492ea805083b96ad4a301b204b5e.pdf
If you're asking, in the context of salience, how strong an indicator-factor relationship should be in order to be considered as functional for defining/identifying the factor, the answer depends on your source and purpose. Here's a potentially useful link:
https://www.amazon.com/Factor-Analysis-2nd-Richard-Gorsuch/dp/089859202X/ref=sr_1_1?crid=NOTK7H7O81O9&keywords=gorsuch+factor+analysis+2nd+edition&qid=1567621980&s=gateway&sprefix=gorsuch+factor+analysis%2Caps%2C137&sr=8-1
Good luck with your work!
Hi Nip Nip,
Precious resources have been shared but I want to add one more. Check this out too;
Montanelli, R. G., & Humphreys, L. G. (1976). Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A Monte Carlo study. Psychometrika, 41(3), 341-348.
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