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I'm currently in the middle of analysing data for a masters dissertation and I'm having a lot of trouble with understanding factor analysis.

I've collected data using a questionnaire in which I divided the questions up into 3 categories, there are a total of 9 items in the questionnaire - 3 questions for each category. My supervisor has told me that factor analysis is the way to go for analysing my set of data, however, I'm struggling to understand why as my research question is focused on how satisfied are a specific demographic with the three categories. Can someone explain to me why factor analysis should be run with this set of data and how it helps to answer my research question? And if exploratory factor analysis is the way to go here? (I don't have AMOS or any other software that can do CFA...)

So far I've run factor analysis on SPSS using varimax rotation (factors seem to be uncorrelated according to the anti-image matrix) and have ended up with 3 components that pretty much reflect the categories that I chose to investigate. Component 2 has the most loadings, followed by component 1 and then 3 and I've given each component a label. Can someone tell me how I can come to answer my research question using these findings? What do the weightings really mean? Can I use this data to find out which component is most important to my demographic and which is least?

Sorry about the overload of questions, I'm really bad at understanding statistics!

[EDIT]

So I managed to get hold of AMOS today and have run CFA to test the 3 factor model that was found from running EFA. After reading around how to interpret the CFA output, I still don't quite understand how it can answer my research question.

My research question aims to look at how satisfied mothers in the education sector perceive themselves to be in areas of maternity policy, flexible work arrangements and opportunities for career development. Using the 3 factors found by running EFA, I drew the 3 factor model on AMOS and it calculated the estimates for me. The model shows a good fit but I'm having trouble understanding the regression weights

  1. Do I look at standardised or unstandardised regression weights?

  2. Are only the significant values (p < .05) important to report? Out of the 9 observed variables, only three from latent variable 1 (career development) and one from latent variable 2 (flexible work) were significant.

  3. Do these significant values mean that they assume most importance in explaining the latent variables?

  4. Will I be able to use these regression weights to answer my research question by assuming the significant observed variables are most satisfactory to my demographic?

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  • $\begingroup$ Some of your expressions sound alarming in that they reveal your confusion over the topic of factor analysis. factor analysis on SPSS using varimax rotation , factors seem to be uncorrelated according to the anti-image matrix, also you may be mixing up principal components with factors, as many do. Certainly, you should read more about FA before you start doing it. $\endgroup$ – ttnphns Aug 14 '14 at 7:02
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Firstly, your supervisor should explain factor analysis to you. That's why he gets paid the big bucks.

But I guess it's up to old CV to plug the gaps of the educational system.

It would be nice if you could get AMOS with your SPSS system, or possibly use sem or lavaan in R, since I think your research question should probably be addressed through confirmatory factor analysis. What SPSS offers is just an exploratory analysis. So far, that seems to have worked well, since it looks as if the analysis produced the three categories that you believe are operative. Note that Varimax will always produce uncorrelated factors. That's what it does.

So what is factor analysis doing? You have a questionnaire with items, but what really interests you are certain underlying characteristics or "categories" that you can't measure directly. You measure these indirectly through the items of the questionnaire. You want the questionnaire to detect those categories. So perhaps questions 1-3 target the first category; 4-6 target the second.

If this model is correct, then the variance matrix of the 9 items will have a particular structure, reflective of the underlying categories. Confirmatory factor analysis lets you test that hypothesis.

Alternative hypotheses could be that all 9 items reflect only 1 category ... or at the other extreme, that there are no underlying categories that can simplify the variance structure. Confirmatory factor analysis would then check that these categories are relevant to the demographic you have.

Factor loadings are sort of the regression coefficients of the items against the underlying factors or categories, if in fact, you could measure those underlying factors. What you get from SPSS, I believe, assumes that the factors are scaled to have variance 1.

I'm not sure that high loadings from a category mean that the category is "important" to your demographic. It does suggest that the factor is present and well manifested by the questions. It also implies that people's responses are very much governed by the factor, and less by randomness. It might help if you specified what these categories are.

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  • $\begingroup$ +1, the point about confirmatory FA being more appropriate is so right... $\endgroup$ – Patrick Coulombe Aug 14 '14 at 3:17
  • $\begingroup$ No one said the supervisor was male.... $\endgroup$ – Nick Cox Nov 5 '14 at 12:13
  • $\begingroup$ The masculine form is standard usage when real world gender is unknown. Take it up on the ESL forum. $\endgroup$ – Placidia Nov 5 '14 at 13:40
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factor analysis - both EFA by SPSS or CFA by AMOS - is used to probe the validity of your questionnaire. This is why your adviser asked you run factor analysis. Your research questions can be probed through analysis of chi-square or crosstabs.

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