Hi Mike,

I think a more robust practice is to do parallel analysis. The technique is very simple you run your FA with principal axis factoring, and then a Monte Carlo simulation for your sample size and number of items in the survey (I use a simple program available for free download). Then you contrast the modeled and observed eigen values, and whe your observed eigen values decrease, you stop retaining factors. 

I am attaching a paper that is helpful for understanding.

Try this, and see if the number of Factors is more parsimonious.

Best,

AM

Hi Mike,

I think a more robust practice is to do parallel analysis. The technique is very simple you run your FA with principal axis factoring, and then a Monte Carlo simulation for your sample size and number of items in the survey (I use a simple program available for free download). Then you contrast the modeled and observed eigen values, and whe your observed eigen values decrease, you stop retaining factors. 

I am attaching a paper that is helpful for understanding.

Try this, and see if the number of Factors is more parsimonious.

Best,

AM

There are several efa factor extraction decision rules. The kaiser (eigen>1) is one but very lenient. Your best bet would be to run a Horn parallel analysis available for free from Marley Watkins' webpage or via spss/sas code from brian o'conner. There you would compare your actual eigen values to the randomly generated e values and retain those that are higher. The next is the minimum average partial test which is available through o'conner's spss/sas program or through r code. Select components when you run the analysis. You also have standard error of scree but that tends to be in between map and pa in terms of leniency. So the three methods are appropriate for your purpose-- kaiser, pa and MAP.

Hey there

I recommend this method

Marcos

Lorenzo-Seva, U. (2013). How to determine the number of common factors using Hull method. Technical Report. Department of Psychology, Universitat Rovira i Virgili, Tarragona.

Hello Ana,Stefan, and Marcos, 

Thank you so much for your answers to my questions!

Since both Ana and Stefan mentioned parallel  analysis for extracting factors,

I would like to look into that first. 

Ana, I just read Matsunaga (2011). It is very helpful!

Thanks for sharing!

Happy New Year to all  !

Best,

Mike

Horn’s PA and Velicer’s MAP have a longstanding research tradition and solid empirical base in factor analysis. Incidentally, Horn’s PA is a critical part of the Hull Method for factor extraction—it utilizes Horn’s PA as the upper bound limit on the number of factors to extract. 

Scree plot is not accurate, and I dont advise you to build your decision on it. 

Eigenvalues is more accurate, the default setting for Eigenvalues  is 1 and above. you can change this for example to 1.5 and above. This depends on the factor analysis outcome.

Thanks a lot for your info, Stefan ! It helps !

No problem.  Also, you should not just arbitrarily adjust your eigenvalue level to suit your needs.  Keep in mind this is EFA, not CFA! Thus, I reiterate the use of Horn's PA, Velicer's MAP and Standard Error of Scree if scree is too subjective (again, available via Marley Watkin's webpage).  Throw in Kaiser (eigenvalue > 1.0) because it is generally the lowest eigenvalue you would use to extract a factor. Good and important post.  Take care and happy new year!

All right, Stefan, thank you so much for your insights and advice!

Happy New Year!

you should base on eigenvalues over than 1 and then see the scree plot (don´t extract factors that scree plot goes very close) - try to extract only the factors with higher eigenvalue

Perhaps it would also be useful to share what is your research objective. Function of that, sometimes it's better to use CFA instead of EFA. Little advice can be given without this information, and automatically believing that EFA is the answer might not always be the best idea...

In simple terms, the larger the eigenvalue, the larger the proportion of variance in the data accounted for by that factor. If a factor has a low eigenvalue, then it is contributing little to the explanation of variances in the variables and may be ignored as redundant. An eigenvalue greater than 1 is considered to indicate the presence of an interpretable factor .

I have a question for those of you who use the Montecarlo simulation method.

After comparing the simulated eigenvalues with the ones generated when selecting eigenvalue >1, do I have to re run the PCA forcing it to generate only the number of factors suggested by the Montecarlo simulation or can I use the same factors scores generated when selecting eigenvalue >1 but only consider the number of factors suggested by the simulation?