hello... my friends
I have one question ...
I am currently researching with factor analysis methods using the SPSS application
what i want to ask is:
when viewing the results of the "Rotated Component Matrix" there is one variable that has a value below 0.5
then, how to overcome the situation?
thank you
It is not 'needing overcoming'; simply a wea-loading item, and a good thing to have in minimum.
Hope this helps
Matt
Hi,
This variable is strongly related to more than one factors. So i propose to go to factor analysis->options and suppress small coefficients. Set this value .50. This way you keep onlly strong coefficients thus variables that clearly belong to one factor.
Best,
Stam
Hello Aurelius,
The answer depends on what your investigatory goal is. If the goal is data reduction, then you may wish to set a very high standard for variable-component salience (affiliation) in order to retain that variable in your set. Be aware that there are plenty of examples wherein much lower thresholds for salience are used (e.g., .30, .40; Raymond Cattell gave an example in which .15 is considered large enough to attend to). So, a variable-component loading of .50 may either be noteworthy or ignorable; it really depends on your purpose.
If the goal is to describe the underlying (latent) variable structure being manifested by the observed relationships among your measured variables, you'd likely be better off using a different factor extraction method than principal components (such as: principal axis, maximum likelihood, alpha, or image), since PCA assumes that: (a) all observed variance is common variance; and (b) there is neither any error variance or unique variance in the data set. Both assumptions are typically not realistic for data sets based on human responses.
Good luck with your work.
David Morse, thanks for taking the time to provide your answer immediately above. I'd like to follow it up with a question: In your view, is it sometimes desirable to have items with a range of loadings, not only high loadings, on a factor (as long as there are no problematic cross loadings) in order to tap breadth of a construct / factor? I am thinking, perhaps of having some items with loadings as low as .40 rather than retaining only the items that have high loadings - say above .65?
I ask because I suspect that having items with only high loadings might encourage redundancy on a scale or subscale.
I'd appreciate hearing about your perspective(s).
Hello Robert Trevethan ,
For many, the idealized factor structure described by Thurstone as "simple structure," represents the easiest (and least likely to be mis-interpreted) solution. Simple structure is the pattern of a variable loading at or near a value of 1 on one factor only (and at or near zero on all other factors). Thus, item-factor affiliation is very clear-cut. Many rotational schemes (e.g., Kaiser's Varimax) attempt to relocate factor axes in space so as to best approximate simple structure patterns.
Your implied question, though, can factors be somehow richer if permitted to have a range of loadings (instead of all being very high only) is an interesting one. I've seen solutions wherein both patterns emerge, and can't really say that one is inherently better in practice. What you could say, though, is that pruning away variables with low or questionable loadings would be one way of making a measure shorter and perhaps yield more reliable scores in future samples. Whether that translates to more valid scores would be an empirical question that likely would depend on the application.
Cheers.
David Morse, thanks for getting back. I can see how "simple structure" is appealing, but I think I'm not wrong in saying that things never (?) turn out that way: Items never have loadings at or near 1 on one factor and zero or near zero on other factors in my experience - though usually I find there is pretty clear separation of items onto different factors with few items that have cross loadings that are < .15, and most items having loadings between about .45 and .90.
Furthermore, in my experience, retaining only the items with high loadings results in items that are similar in overt appearance and that produce extremely high coefficient alpha values - so, it seems are essentially redundant.
Thanks for musing with me on this.
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