Elahe, SPSS uses the Kaiser-Guttman criterion for deciding on the number of factors, which means that all factors with eigenvalues > 1.0 are selected. This is problematic, because this criterion often chooses too many factors. It would be better to also rely on the scree plot and the parallel analysis. A scree plot displays the eigenvalues associated with a component or factor in descending order versus the number of the component or factor. The point where the slope of the curve is clearly leveling off (the “elbow) indicates the number of factors that should be retained.

The parallel analysis is a method based on the generation of random variables. In this procedure, eigenvalues from a data set prior to rotation are compared with those

from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. This method is not included in SPSS, but you could use an online resource, such as http://ires.ku.edu/~smishra/parallelengine.htm.

If you have strong theoretical reasons, you may also opt to check the button 'fixed number of factors' and put your desired number of factors in the box, e.g., 3 or 5, and investigate the the loadings on each component or factor whether they make sense.

Eigenvalues of .1 or .3 are very small, I don't know where you got this information from. It doesn't seem to be correct.

Here is an online resource which may help:

http://www.unt.edu/rss/class/Jon/SPSS_SC/Module9/M9_PCA/SPSS_M9_PCA1.htm

Regards, Karin

Elahe, SPSS uses the Kaiser-Guttman criterion for deciding on the number of factors, which means that all factors with eigenvalues > 1.0 are selected. This is problematic, because this criterion often chooses too many factors. It would be better to also rely on the scree plot and the parallel analysis. A scree plot displays the eigenvalues associated with a component or factor in descending order versus the number of the component or factor. The point where the slope of the curve is clearly leveling off (the “elbow) indicates the number of factors that should be retained.

The parallel analysis is a method based on the generation of random variables. In this procedure, eigenvalues from a data set prior to rotation are compared with those

from a matrix of random values of the same dimensionality (p variables and n samples). PCA eigenvalues from the data greater than PA eigenvalues from the corresponding random data can be retained. This method is not included in SPSS, but you could use an online resource, such as http://ires.ku.edu/~smishra/parallelengine.htm.

If you have strong theoretical reasons, you may also opt to check the button 'fixed number of factors' and put your desired number of factors in the box, e.g., 3 or 5, and investigate the the loadings on each component or factor whether they make sense.

Eigenvalues of .1 or .3 are very small, I don't know where you got this information from. It doesn't seem to be correct.

Here is an online resource which may help:

http://www.unt.edu/rss/class/Jon/SPSS_SC/Module9/M9_PCA/SPSS_M9_PCA1.htm

Regards, Karin

Dear Karin

You have been a great help to me esp. for varimax rotation and PCA. Thank you so much.

I have two more questions yet, if you don't mind.

1. what to do with items which are loaded under more than a factor after rotation? (what if they are among the two items which create a component and based on the information in the link need to be removed? are they removed from both components ?

2. How many times do we repeat rotation? Is it till we find components with max 3 items?

again i am so grateful

Elaheh

Elaheh, if you have cross-loadings, you could try different rotation methods, e.g., promax and oblimin, and check whether different solutions are provided. You could also increase the number of factors to be extracted. Does this item now load onto a separate factor? Try as much as you like, you will get a pattern of results, most rotation methods will result in similar solutions.

If you are developing a new questionnaire, you may think about removing one of the items, not both - this should be guided by theory. If the questionnaire already exists, you should not eliminate items.

What is you aim? To develop a new questionnaire?

Regards, Karin

Dear Karin, as I said I have used a questionnaire (on classroom assessment practice and value) developed originally in the context of UK with 3 components/clusters. I planned to validate it in the Iranian context and see which items don't work and which ones measure a different construct. In EFA i came up with 10 components which explained 63% of the variance (the first component 19.39%).  I want to know if the same constructs/components are identified in the Iranian context. In fact my first research question is this questionnaire has an acceptable index of validity in this context. I have also run interviews to know which assessment practices the participants/teachers employ in their classes. The interview questions were based on the three UK constructs and in the interview the participants were more inclined to the first factor. 

I have read the article Warwick, Shaw and Johnson (2015) in which the same questionnaire was validated in the non western context (5 countries but not Iran) and they used EFA  which could derive the first two components and one different third component. " The varimax rotation method was used here to maximize the dispersion of loadings within factors....... the generation of dimensions from the data set took into account only those teacher practice items which achieved promary factor loadings of ore than .3 and which did not load on to more than one dimension/factor" they write in their article. 

With the varimax rotations i came up with the same item loadings and the problem i have is which items under which components to keep.

Best wishes along with sincere appreciation for your time and guidance

Elaheh

Elaheh, now I understand your questions and your research aims better. When you say "In EFA i came up with 10 components" I guess that you used the Kaiser-Guttman criterion, i.e. you retained all components with eigenvalues > 1.0? This is the default in SPSS, but you should not use it without taking alternatives into account. Just keep in mind that with this method often too many components are extracted. Try the parallel analysis in order to investigate, whether your 10 dimensions are justified.

The next point concerns varimax rotation. Which method did you use after extracting the components? Did you again use PCA? You say that you used EFA, which seem to imply that you used some method like principal factor analysis (PFA). SPSS always performs a PCA for determining the number of components, irrespective of the method chosen by you. If you think that your factors are latent variables, you should use EFA (PFA) and not PCA. But if you think that components are okay, which means that you just intend to get linear combinations of items, which do not have to measure the same construct, PCA would be fine. With EFA, it would be better to use an oblique rotation method. If the factors are actually uncorrelated, the oblique rotation would result in uncorrelated factors.

Now If you have some crossloadings, this often occurs when your factors are actually correlated but you used an orthogonal rotation method. If the crossloadings cannot be eliminated by using a different number of factors or by using a different rotation method, you may think about eliminating the items but this would reduce your item pool.

But if you opt to keeping all items because of theoretical reasons, and you just want to know which items should be summed up to form a scale, one would usually use all items with higher loadings on this factor. You cannot use an item twice, because then the contents of the scales would be redundant.

Generally all items with the highest loadings on a factor are summed to form a scale, and from items with crossloadings the higher loading (primary loading) is used to decide to which scale the item should be added. The decision which items to keep are often based on the size of the factor loadings. There exist some 'rules of thumb' about the size of the factor loadings. Loadings higher than .30 (which is equivalent to ca. 10% explained variance) or loadings higher than .40 (which is equivalent to ca.15% explained variance) are regarded as important or relevant.

Good luck with your research!

Regards, Karin

Number of factors can be decided  on the basis of egien value>1, using scree plot and  some times, we can decide on the basis of the % of variance explained by factors  but the same time you have to see the  eigen value also. After rotation, If items are loaded with more than one factors, you should check questionnaire 

[Edited]

This might be a misunderstanding, but when speaking of "validation" you should not use "EFA" at all, but Confirmatory Factor Analysis. You have a theory, there is a hypothesis, given from previous findings (There are factors x,y,z; we hypothesize that they are also present in Iran.) - So the first step would be, test if it "works" at all, and afterwards maybe, find out which items might not "work".

On a more methodological level, the approach you are going is somehow odd, because a PCA only reduces variance (binning as much items together as possible), and not detects latent factors, as Karin points out.(A good example would be to run a PCA over a data set which contains processing times of single pages in an (arbitrairy chosen) online survey. A PCA will find a main component, binning together the information that people are quicker or slower in answering specific questions, e.g. long questions, short questions etc.. And this component will "explain" a huge amount of variation. However, when you do a PFA (axis analysis) you will not find any of such factors at all, because in this case there will be no correlations at all between the processing times of the pages, which would indicate systematic variation on a latent dimension.)

In some cases, PCA and PFA produce redundant results (you need to check both), but this mainly depends (among others) on if there are any factors at all, how strong they are, how many of them there are actually, and on the size of the item-set. Using PCA needs consideration of the following fact: Roughly said an Eigenvalue = 1 means that a component or factor can explain the variance of 1 item. You see, the bigger the item-set, the more components (especially) will be found according to the Kaiser criterion, because all items explain their own variance first and are therefore a 'linear combination of themselves' and some 'shared' error, thus eigenvalues will be normally distributed around 1, when there is no latent factor. If you want to stick with the EFA, do as Karin says and use a scree plot :).

Oh and, if you are using a Principal Factor (Axis) Analysis, there is actually no need for rotation, because it is done already by definition (the most common axis is calculated), however, consider oblique rotation (e.g. promax), as Karin points out too, to check for correlated factors, if there is any theoretical reason for it. If the factors are not correlated, oblique rotation yield the same results as rotated orthogonal axes.