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.
Some studies (such as Hair, Black, Babin, & Anderson, 2010) suggest that loadings of the items should be at least .50 and ideally .70. Higher loadings indicate that items are strongly related to latent variables. R2 values express items' variance explained by the latent factor. R2 values are the squared factor loadings in CFA model. Referring to Hair et al.'s work, the items with R2 below .25 are candidate for removal.
Good luck with your work..
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