Hello Samil,

Thanks for the extra explanations. They help.  I love poring over the kind of output that you've provided, but sometimes it's good to be aware of the fuller picture and the nature of any other analyses that have been conducted - and I might still be in the dark too much.

From this distance, the fact that you have a loading of .37 isn't particularly troubling.  It's pretty close to a cutoff of .40 - which is an arbitrary cutoff anyway. 

But I'm fascinated by other things in your results, e.g., that you have three factors and that on the first of them you have moderate loadings but a pretty high alpha, on the second you have moderately high loadings and a low alpha, and on the third you have high loadings and a very high alpha.  From this distance, I have a sense that something strange is going on, but I'm not sure what it might be.

The pattern and values of your coefficient (i.e., Cronbach's) alphas trouble me a bit. In your third set of items, the high alpha suggests that you are asking much the same kind of question repeatedly as far as your respondents are concerned, so there's not a lot of "richness" in the factor. I wonder whether the same is happening, but to a lesser extent, in your first factor. And your second factor seems to have items that are heading a bit too much in different directions given the alpha value.

I think this is related to something I quoted in an article published in 2009: It has been recommended that “as with food and other good things, moderation in internal consistency is best”.

If researchers aim for a moderate amount of association among a set of items, alpha values of approximately .65 are probably satisfactory for four or five items, whereas alpha values of approximately .93 are equally satisfactory for approximately 30 items. In line with this, alpha values of approximately .75 and .80 would be appropriate for ten and 15 items, respectively. (I can give you the reference for this article if you're interested, but you mightn't be; it's primarily about the development of self-referent instruments, but deals with a number of aspects of scale development, including the basics of factor analysis.)

This makes me wonder whether you might be shoehorning your results (I like the expression; haven't heard it before; can't wait to use it somehow) too much to fit the previous instrument when you might need a bit of a fresh start.  Did your initial analyses tell you that you had three factors?  If not, I wonder whether that's why you're getting some of your results.  Also, have you tried both orthogonal and oblique rotations?  Have you even rotated the data?

I hope this is all helpful.  Factor analysis can be tricky and subjective in a number of respects - which makes it both frustrating and fun.

Robt.

Dear Sunil,

I could be wrong, but I suspect that the table you have attached is a composite of the results from SPSS (or whatever stats package was used) output.  It appears that the authors have listed the different factors (six of them in this case) down the left-hand side of their table and have then provided the highest loadings that pertained to each of those factors' items that they drew across from the computer output. They presented their results this way rather than providing a table that reflected the original output, which would have contained a number of separate columns with factor loadings. They might have presented their results this way to save space.

In essence, you don't need to ask for something other than you probably have already. You just would need to collapse the results of something like your rotated component matrix to a single column.

Does that make sense? Please feel free to come back with more queries or if you don't understand what I am getting at.

For what it's worth, I often see results from factor analyses presented in a different way from the way you've attached - i.e., with the factors and items listed on the left BUT with several columns to the right showing all the loadings.  I find that more revealing (and reassuring).

Robert.

after the communality table there is communality matrix and after that comes rotated component matrix (provided you have given this command), which illustrates the factor loading for each variable

Dear Sunil

Pl see the attachment. May be of some help.

Regards

Rajiv

Chapter A note on the Factor Analysis in Forestry Sciences

Thanks Robert. Your answer was helpful.

One item in my scale has shown low factor loading but the same item when combined with other two items in the construct shows acceptable Cronbach alpha (.70).

Should the item be retained or eliminated from further analysis?

Hello Sunil,

I'm glad my answer was helpful.  Sorry, but I don't quite understand your situation, particularly the wording "when combined with other two items". [I think you mean "two other" - yes? - but that's not the issue.]  

From what you have written, I am not quite sure what's going on. I was assuming, from the output that you put with your original question that you have more than one factor in your data, but that might be an incorrect assumption.

Did you discover, for example, that you have only one factor on which 11 of the 12 items loaded quite nicely, e.g., > .40?  Also, how low was the loading on the item you refer to? 

Forgive me for asking if it's not necessary to do so, but did you obtain a scree plot, and were your KMO index and Bartlett's test of sphericity OK?  And did you have enough participants - at least 120 in your case - to run a factor analysis? Did your scree plot suggest that there was only one factor in your scale?  If there was more than one factor, have you tried different ways of conducting your factor analyses that might produce a cleaner solution than you originally obtained? If you used an oblique rotation until now, things might shake out a bit differently if you used an orthogonal rotation, restricting the solution to two factors in both cases.

I hope these questions make sense. Please feel free to let me know if not and I can explain further.

If you had only one single factor within your 12 items, I'd be inclined to look for a slightly higher Cronbach's alpha than .70, and that might be a reason to drop the low-loading item.

If you felt inclined, feel free to attach your rotated matrix and even the results from your Cronbach's alpha analysis, and I might be able to offer some more advice.

Robt.

Apologies I was not clear in my query. Let me try again....

I have a 12 item scale (made up of 3 subscales) on Attitude towards sports sponsorship. I adapted the scale for my research from a previously published scale that had shown to have good Reliability. KMO is fine and sample size is also adequate. Note I am not trying to do a cross validation of earlier reported factor structure because it was done with a different sample/region etc. That is why I modified the scale and have to reassess reliability and calculate factor loadings.

The results I get are attached. In the attached table, you will see that the subscale reliability for "Attitude towards event" is 0.73 BUT the factor loadings for each of the items is low.

My question is for analysis, can I retain the items with low factor loading because the subscale of items reliability (.73) meets minimum alpha guidelines (.70)?

I do realize I am trying to shoehorn the results of my modified scale into the original scale factors (which may be the problem) but if I do want to use the "Attitude towards event" subscale as shown because it has adequate Reliability, can I do this and ignore the Factor Loading?

Hello Samil,

Thanks for the extra explanations. They help.  I love poring over the kind of output that you've provided, but sometimes it's good to be aware of the fuller picture and the nature of any other analyses that have been conducted - and I might still be in the dark too much.

From this distance, the fact that you have a loading of .37 isn't particularly troubling.  It's pretty close to a cutoff of .40 - which is an arbitrary cutoff anyway. 

But I'm fascinated by other things in your results, e.g., that you have three factors and that on the first of them you have moderate loadings but a pretty high alpha, on the second you have moderately high loadings and a low alpha, and on the third you have high loadings and a very high alpha.  From this distance, I have a sense that something strange is going on, but I'm not sure what it might be.

The pattern and values of your coefficient (i.e., Cronbach's) alphas trouble me a bit. In your third set of items, the high alpha suggests that you are asking much the same kind of question repeatedly as far as your respondents are concerned, so there's not a lot of "richness" in the factor. I wonder whether the same is happening, but to a lesser extent, in your first factor. And your second factor seems to have items that are heading a bit too much in different directions given the alpha value.

I think this is related to something I quoted in an article published in 2009: It has been recommended that “as with food and other good things, moderation in internal consistency is best”.

If researchers aim for a moderate amount of association among a set of items, alpha values of approximately .65 are probably satisfactory for four or five items, whereas alpha values of approximately .93 are equally satisfactory for approximately 30 items. In line with this, alpha values of approximately .75 and .80 would be appropriate for ten and 15 items, respectively. (I can give you the reference for this article if you're interested, but you mightn't be; it's primarily about the development of self-referent instruments, but deals with a number of aspects of scale development, including the basics of factor analysis.)

This makes me wonder whether you might be shoehorning your results (I like the expression; haven't heard it before; can't wait to use it somehow) too much to fit the previous instrument when you might need a bit of a fresh start.  Did your initial analyses tell you that you had three factors?  If not, I wonder whether that's why you're getting some of your results.  Also, have you tried both orthogonal and oblique rotations?  Have you even rotated the data?

I hope this is all helpful.  Factor analysis can be tricky and subjective in a number of respects - which makes it both frustrating and fun.

Robt.

Hi Robert,

I took your suggestion and ran a Oblique Rotation and YES!!!! the factors now load correctly as hypothesized in original scale (with exception of one item which I will eliminate).

Question: In the Oblique Rotation Output,I see 3 Matrix: Component, Pattern, Structure. Which Matrix should I use to report the Factor Loadings?

THANK YOU for your help with this.

p.s. I am interested in Scale Development as one of my interests, and would like to read your article that you referenced in your post.

Sunil

Hello Sunil,

I'm delighted that you obtained what seems to be a more satisfactory solution.  In my experience, orthogonal (e.g., varimax) rotations often produce the most satisfactory and clean solutions, but sometimes it's a case of testing the waters in different ways and seeing what seems to be most reasonable theoretically as well as statistically.

I'm pretty sure you should use the pattern matrix as the basis for your interpretation and reporting of loadings and factors (it's a long while since I was running factor analyses - about 8 years - so I've gone a bit rusty on what used to be totally automatic for me).  Maybe check out some YouTube sites concerning factor analysis.  There are a number of them, and most of them are really helpful.  I'd recommend that you look at several of them and note the commonalities to ensure you are on the right path.

My article about scale development is the following:

Trevethan, R. (2009). Self-assessment of foot health:  Requirements, issues, practicalities, and challenges. Journal of the American Podiatric Medical Association, 99, 460-471.

Although it's based on measurement of foot health, the principles that I deal with are much more general in nature.  There is a little bit in there about factor analysis.

Robt.

Dear Sunil,

You may find my guide helpful:

https://www.researchgate.net/publication/304490328_Advice_on_Exploratory_Factor_Analysis

Working Paper Advice on Exploratory Factor Analysis