I have read that Cross-loadings of below .3 are often ignored! Can I have some reliable references to back this up please?
I have read exisiting work and authors tend to make this decision without supporting their decision!
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A factor loading of $0.30$ means that approximately $10$% of the variance in the indicator is explained by the factor (i.e., $0.30^2=0.09$). Loadings lower than this are often considered unreliable or unimportant. The extent to which model fit is affected by constraining such loadings to $0.00$ can be explored using confirmatory factor analysis (CFA). I wouldn't call this approach "ignoring" them but maybe you had a different approach in mind. If so, please clarify in the question.
Edit: In the comments below, I provide some possible citations. Since you seem to want a more empirical treatment of this issue, I recommend Peterson (2000).
answered Mar 20, 2017 at 14:20
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$\begingroup$ Thanks Jeffrey. You are absolytely right in saying that. However, when I tried to find a reliable source / reference for citation in my work - It wasn't easy. Can you give a reference or two that I can cite please? $\endgroup$ Mar 20, 2017 at 14:37
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$\begingroup$ It's hard because this is more of a scientific convention than a rule or law. However, you can cite that this convention has been in use for a very long time indeed: Fabrigar, L. R., Wegener, D. T., MacCallum, R. C., & Strahan, E. J. (1999). Evaluating the use of exploratory factor analysis in psychological research. Psychological Methods, 4(3), 272–299. $\endgroup$ Mar 20, 2017 at 14:47
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$\begingroup$ Also very relevant: Peterson, R. A. (2000). A meta-analysis of variance accounted for and factor loadings in exploratory factor analysis. Marketing Letters, 11(3), 261–275. $\endgroup$ Mar 20, 2017 at 14:50
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$\begingroup$ "[I]t seems from the general literature in the social and behavioral sciences that [a threshold factor loading of] 0.30 [is the minimum that is traditionally used when deciding to] accept an item or variable as belonging to a factor or component" -- (p. 160). Merenda, Peter F. (1997). "A Guide to the Proper Use of Factor Analysis in the Conduct and Reporting of Research: Pitfalls to Avoid," Measurement and Evaluation in Counseling and Development 30, 156-164. $\endgroup$ Mar 20, 2017 at 14:53
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$\begingroup$ Thank you very much. That was exactly what I was keen to get hold of. $\endgroup$ Mar 20, 2017 at 15:01