Hello Nazanin,

It depends on: (a) how many factors there are in your chosen solution; (b) if more than one factor, whether you rotated the solution using an orthogonal rotation (e.g., varimax) or an oblique rotation (e.g., promax, oblimin).

If only one factor, the "initial solution" matrix shows variable-factor loadings.

If two or more factors and orthogonal rotation, the "rotated factor matrix" shows the loadings.

If two or more factors and oblique rotation, the "structure matrix" shows the loadings.

Good luck with your work.

Both rotated and unrotated factor Matrices gotten from PCA are the table of results for factor analysis. The initial solution could be firstly done to see how each factor will rotate well.

Dear Nazanin Tangestanizadeh

in addition to David Morse 's answer, I would recommend reading up on this issues in a textbook for further understanding, as I believe this to be a "textbook question". For example:

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th. Ed.). London: SAGE.

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis: A global perspective (7th. Ed.). Upper Saddle River, NJ: Pearson.

Best

Marcel

If you have run PCA with Varimax, refer to rotated component matrix. If you have run MLM with run Promax, refer to pattern matrix.

Nazanin Tangestanizadeh, I'm aware that you are being given different kinds of advice in response to your question.

First, I note that you indicated you are conducting factor analysis, which, to me, means you're not conducting principal factor analysis (PCA), which is a slightly different procedure. Therefore, the response from Imran Anwar is good in some respects, it might not be a good match for your needs. However, factor analysis and PCA often yield highly similar results, so his advice is worth considering.

Second, you've not indicated how many factors you obtained or, if you obtained more than one factor, whether, or how, you rotated the factors. All of those things are important for people who want to help you.

Third, I hesitate to offer different advice from David Morse because I respect his knowledge and advice highly, but in my experience the most appropriate loadings to report following an oblique rotation of factors are the loadings in the pattern matrix, not the structure matrix. David, I'd be happy for you to challenge me on this if you care to do so. :-)

Well, after the advice given by experienced researchers such as David Morse and Robert Trevethan, I don't see a need for further advice. I can only support them!

For example, Robert is right in saying that PCA and Factor analysis (often referred to as EFA) are slightly different. Many people confuse them and refer to them interchangeably mainly because both are found under the same menu in SPSS.

Moreover, I am looking forward to David's rebuttal on Robert's saying " the most appropriate loadings to report following an oblique rotation of factors are the loadings in the pattern matrix, not the structure matrix." I have been looking at the pattern matrix as well. So, looking forward to an interesting discussion here :).

Ali Farooq, thanks for pursuing this. As you point out, people confuse PCA and factor analysis - by which, in this context, refers to exploratory factor analysis (EFA) - not confirmatory factor analysis.

However I suspect the confusion between PCA and EFA arises because the default option for Extraction under Factor in SPSS is principal components. Why SPSS doesn't remove that prospect for misconception mystifies me.

Like you, I have always gone to the pattern matrix for interpreting the results of an oblique rotation because of advice I've seen in a number of sources. I will confess, also, that it's the pattern matrix (not structure matrix) loadings that I've reported in my own publications. I have almost always found the pattern matrix easier to interpret (i.e., it produces the more "logical" factor structure), though I am aware of some researchers referring to the structure matrix results.

I don't know whether it's correct or not, but on the following site: https://www.ibm.com/support/pages/pattern-matrix-and-structure-matrix-definition-spss-factor-output#:~:text=The%20pattern%20matrix%20holds%20the,a%20function%20of%20the%20factors.&text=The%20structure%20matrix%20holds%20the%20correlations%20between%20the%20variables%20and%20the%20factors

I found this: "The pattern matrix holds the loadings. ... The structure matrix holds the correlations between the variables and the factors."

Maybe that helps.

Marcel Grieger, thanks for suggesting the Hair et al. (2010) book. I've just checked it, and at the top of page 117 the authors wrote:

If an oblique rotation has been used, two matrices of factor loadings are provided. The first is the factor pattern matrix, which has loadings that represent the unique contribution of each variable to the factor. The second is the factor structure matrix, which has simple correlations between variables and factors, but these loadings contain both the unique variance between variables and factors and the correlation among factors. As the correlation among factors becomes greater, it becomes more difficult to distinguish which variables load uniquely on each factor in the factor structure matrix. Thus, most researchers report the results of the factor pattern matrix.

I have added some bolding that might be helpful. That might shed some light on the issues in this thread.

Hello All,

For oblique solutions, the structure matrix shows correlations of variables and factors. The stronger the factors are correlated, however, the more the structure coefficients (loadings) carry that information as well as unique relationships of variables and factors. The pattern matrix carries information about unique contribution/emphasis of variables in the construction of factors (correlations among factors being accounted for).

I agree that looking at pattern matrix is helpful (I do it all the time), and that it takes into account the correlations among factors. However, Nazanin's original question was, "...which table of results in spss refers to the factor loadings."

Stay safe!

David Morse, thanks for getting back. For what it's worth - and I confess I'm not sure it's directly related to what you've posted - I've just gone to five sets of EFA output in research I'm associated with - each set with different participants.

In all cases, parallel analysis had strongly suggested there were only two factors in the data.

In four of the five cases, the correlation between the factors was in the high .70s, and in the fifth case, it was in the high .50s - so in all cases, the factors were quite highly related to each other.

In all cases, the pattern matrix provided loadings that were much more interpretable than were the loadings in the structure matrix. I base that on the overt (i.e., verbal) content of the items as well as on the number and extent of cross loadings. There were a lot more, and closer, cross loadings within the structure matrices.

Of course, this is only a small sample of EFA outputs. I would be interested to see what other researchers have found in their analyses - particularly if the correlations between the factors was lower than in the data I've referred to above.

To grasp the what and why of factor analysis (FA) using SPSS, you could check out the annotated SPSS FA output by IDRE Stats (see the link below).

Factor analysis | SPSS annotated output. (2021). IDRE Stats—Statistical Consulting Web Resources. https://stats.idre.ucla.edu/spss/output/factor-analysis/

Good luck,

Mohialdeen Alotumi, the site you've provided in your post above could well be useful for some people, but some of its contents concern me.

First, I think it would be helpful if the author indicated that the extraction communalities are the communalities to pay most attention to. Furthermore, perhaps it would have been helpful to indicate that extraction communalities > .50 are desirable, with those < .30 being undesirable. In fact, throughout the site, I find there is an unfortunate lack of information about appropriate decision making and what should be highlighted when reporting exploratory factor analyses.

Second, the scree plot suggests that there are two, not three, factors in the data, and the eigenvalues suggest the same. I think that should be mentioned. Also, given that use of the Kaiser criterion (eigenvalues > 1) has been criticized for at least 20 years and scree plots, although often helpful, are often ambiguous, I think it would have been good if mention had been made of other methods for identifying the likely number of factors in the data. Parallel analysis is one such method.

Third, I can't see why, despite the Kaiser criterion and scree plot, three factors were extracted. My hunch is that two factors should have been extracted, in which case the third factor would have been seen as too weak to persist with.

Fourth, I'm not sure why an orthogonal (varimax) rotation was used. The matrix showing the correlations between the factors (shown near the bottom of the output) indicates that the factors were quite strongly correlated with each other. Surely, therefore, an oblique rotation would have been more appropriate. I mention this because many researchers persist in using a varimax rotation with their data despite strong recommendations for at least 20 years that oblique rotations are almost always more appropriate. Using a varimax rotation in the example is likely to perpetuate an undesirable practice.

Fifth, there is no indication of an iterative process being useful - a process that is likely to have removed the two items at the bottom of the list or to have resulted in additional items being generated for that factor to make it more substantial for evaluative purposes.

Apart from that, and in light of issues raised higher up in this thread, I think it's interesting that the pattern matrix for the oblique rotation provides a cleaner basis for interpretation than does the structure matrix.

Robert Trevethan, thanks for such a detailed concern. You could kindly forward it to UCLA since they have a link at the bottom of the page for reporting any issue. That being said, I believe the page could serve answering our lady's enquiry, "I want to know which table of results in SPSS refers to the factor loadings?"

Best,

Mohialdeen Alotumi, you're welcome. In fact, I have not only contacted the folk responsible for the site, but have also received a courteous (and very rapid) response from a person there. That person acknowledged that the contents of the site could well be out of date by at least 10 years and also mentioned that he and his group are operating under budgetary and personnel constraints that limit the nature and quality of the material they produce.

The person also wrote that the sites such as the one at hand "are merely descriptive pages meant to explain output". Let's accept that!

As far as the original question on this thread is concerned, I think that it might or might not have been answered to the questioner's satisfaction. For me, there was too little information in that question for others to be able to help her with confidence. Here's hoping we did help.

Please refer to my publication on scale development. It is mentioning EFA and CFA on the items extracted through the review of the literature.

Here is the link of the article.

http://ajss.abasyn.edu.pk/admineditor/papers/V11I1-1.pdf

Thanks