Reference for factor loading cut-off
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Reference for factor loading cut-off
 
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Re: Reference for factor loading cut-off
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The is nothing in Holy Scripture about a
cutoff point. Some say at 1.0, your journal editor says 0.5, some say no such
rule makes sense. So you better think by yourself what makes sense according to
your theory about the underlying factors that explain your observed variables. Hector From: SPSSX(r)
Discussion
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Re: Reference for factor loading cut-off
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In reply to this post by E. Bernardo
Of course a lot depends on the specific context of your analysis. Is
this for a check on the key for a pre-existing scale? is this a purely
exploratory analysis without the variables being written to measure a
particular construct?
If you are developing a key for a summative scale, that is a reasonable cutoff for the main loading although .4 is not terrible as long as the items are loading cleanly, i.e., not over .3 or so on another factor. A cutoff of .5 would assure that items were clearly related to the factor. I would wonder about the interpretation of a factor Art Kendall Social Research Consultants Eins Bernardo wrote:
Art Kendall
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Re: Reference for factor loading cut-off
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In reply to this post by E. Bernardo
Two questions: why principal components and why a varimax
rotation? As far as cut-offs go, why not test them. Some people use 1/sqrt(N-3)
as an estimate of the standard error. There are programs that do significance
tests of loadings for EFAs, like Mplus. Dr. Paul R. Swank, Professor and Director of Research Children's Learning Institute University of Texas Health Science Center-Houston From: SPSSX(r) Discussion
[mailto:[hidden email]] On Behalf Of Eins Bernardo
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Re: Reference for factor loading cut-off
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In reply to this post by E. Bernardo
Quoting Eins Bernardo <[hidden email]>:
> I am working PCA using varimax rotation. The editor of a journal > sugge> sted a cut-off of 0.5 on the rotated factor loadings. Using > that cut-off is the same as throwing my paper into the garbage can since > only few variables would qualify such criterion. I am looking for > a reference about the cut-offs. I appreciate your help. > The default cutoff in SPSS factor analysis for "small coefficients" is 0.10, but these cut-offs are just arbitrary values chosen to make the output of the procedure neater and easier to understand. Nevertheless, 0.50 seems an absurdly large value to choose. I am sure that references could be found which would offer suggestions, but they would just be general guides rather than scientific choices appropriate to your analysis. You might think of a similar problem of deciding which regression coefficients are greater than zero so that you can simplify a model by dropping variables which do not play a significant role in the equation. You don't do this by choosing an arbitrary value such as 0.10 or 0.25, but you compare the cofficient with its standard error, and you just leave the significant ones in the model. SPSS factor analysis doesn't give you standard errors or tests of whether some coefficients are not significantly different from zero. For that you need something more sophisticated (and, alas, a bit harder to use) such as AMOS, where standard errors are available. David Hitchin ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Reference for factor loading cut-off
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In reply to this post by E. Bernardo
Eins,
There is no gold standard for factor loadings. Requiring a loading to be .5 is asking that 25% of the variance on the item be shared with the factor, which is pretty stringent. A more common cutoff is .4 (16% shared variance), and I have often seen .3 or .35 used. The editor may be inclined to use a more stringent criterion if your analysis was based on principal components, rather than principal factors, because the estimated loadings would be higher (that said, .5 is still a bit high). You might want to consider using Confirmatory Factor Analysis on your data, rather than Exploratory Factor Analysis, because you can at least appeal to the fact that CFA computes standard errors for the loadings, applies inferential statistics, and indicates which loadings meet a criterion for statistical significance. You may be able to make a case for including all of the loadings that are statistically significant, even if they are below .5 The issue of whether the loadings are large enough to be of practical significance still remains, of course, but that is a substantive issue dealing with the subject you are studying. In many areas of research, accounting for 16% of the variance in an item with a factor is not bad. HTH, Stephen Brand ---- Eins Bernardo <[hidden email]> wrote: > I am working PCA using varimax rotation.� The editor of� a journal suggested a cut-off� of 0.5 on the rotated factor loadings.� Using that cut-off is the same as� throwing my paper into� the garbage can� since only few� variables would qualify such criterion.� I am looking for a� reference� about the cut-offs.� I appreciate your help. > � > Eins Try cool new emoticons, skins, plus more space for friends. Download Yahoo! Messenger Philippines now! http://ph.messenger.yahoo.com -- For personalized and experienced consulting in statistics and research design, visit www.statisticsdoc.com ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Reference for factor loading cut-off
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I seem to remember reading about a graduate student at Wharton loading random numbers into a factor analysis and coming out with factor loadings of about .5. I cannot remember where I read that. My memory may be failing me.
RG Rodrigo A. Guerrero | Director Of Marketing Research and Analysis | The Scooter Store | 830.627.4317 -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Statisticsdoc Sent: Tuesday, March 10, 2009 10:53 AM To: [hidden email] Subject: Re: Reference for factor loading cut-off Eins, There is no gold standard for factor loadings. Requiring a loading to be .5 is asking that 25% of the variance on the item be shared with the factor, which is pretty stringent. A more common cutoff is .4 (16% shared variance), and I have often seen .3 or .35 used. The editor may be inclined to use a more stringent criterion if your analysis was based on principal components, rather than principal factors, because the estimated loadings would be higher (that said, .5 is still a bit high). You might want to consider using Confirmatory Factor Analysis on your data, rather than Exploratory Factor Analysis, because you can at least appeal to the fact that CFA computes standard errors for the loadings, applies inferential statistics, and indicates which loadings meet a criterion for statistical significance. You may be able to make a case for including all of the loadings that are statistically significant, even if they are below .5 The issue of whether the loadings are large enough to be of practical significance still remains, of course, but that is a substantive issue dealing with the subject you are studying. In many areas of research, accounting for 16% of the variance in an item with a factor is not bad. HTH, Stephen Brand ---- Eins Bernardo <[hidden email]> wrote: > I am working PCA using varimax rotation. The editor of a journal suggested a cut-off of 0.5 on the rotated factor loadings. Using that cut-off is the same as throwing my paper into the garbage can since only few variables would qualify such criterion. I am looking for a reference about the cut-offs. I appreciate your help. > > Eins Try cool new emoticons, skins, plus more space for friends. Download Yahoo! Messenger Philippines now! http://ph.messenger.yahoo.com -- For personalized and experienced consulting in statistics and research design, visit www.statisticsdoc.com ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD The information transmitted is intended only for the addressee(s) and may contain confidential or privileged material, or both. Any review, receipt, dissemination or other use of this information by non-addressees is prohibited. If you received this in error or are a non-addressee, please contact the sender and delete the transmitted information. ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
Re: Reference for factor loading cut-off
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In reply to this post by David Hitchin
It seems that the question of desirable loading size is tied up with the
issue of the sample size on which the analysis is done. The source for the rules of thumb below is James Stevens' Multivariate Analysis textbook and citations therein. These rules would apply when the correlation matrix is being analyzed and PCA is the method of analysis: Components with 4 or more loadings above .6 in absolute value are reliable regardless of sample size. Components with about 10 or more loadings of .4 are reliable as long as N > 150. Components with only a few low loadings should not be interpreted unless N > 300. Here is another rule. Use the following formula: n=302500/(500*Y+60*v-33)**2 where Y is the average distance between a sample and population loading, v is the hypothesized population loading, and n is the sample size required. For example, if an average loading is 0.5 and you wish to observe a discrepancy at least as small as .05 between your hypothesized loading and the sample-based one, you would need a sample size of at least 625. You can see in the above formula that smaller average loadings lead to larger required sample sizes, as does a smaller desired discrepancy. Tony Babinec [hidden email] "I believe the blues, the way things are today, is more important than it ever was." B.B. King ===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD |
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