Exploratory Factor Analysis versus Confirmatory Factor Analysis

First of all, confirmatory analysis is carried out, and if it seems that the goodness of fit is low, I think that exploratory factor analysis should be carried out.

Both techniques have the purpose of uncovering latent factors. You should only do an EFA if your instrument has never been explored before. The aim of CFA is to confirm to what extent your model fits the data. Maybe this link culd be useful for you!

Dear 

If you need to conduct translating to your measures from language to another language I suggest to use EFA and then CFA. Without translation, you can use only CFA.

General rule: EFA > Used for instruments (or scales) that have never been tested before (for their validity are reliability). CFA > Used for instruments (or scales) that have been tested before (for their validity are reliability).

I argue that when you translate an existing instrument (or scale) (that has been tested before for its validity are reliability), in order to use it in another country (different language), this instrument (scale) becomes “new”. So, you need to perform EFA.

Moreover, I argue that when you use an existing instrument (or scale) (that has been tested before for its validity are reliability) in the same country (same language), but in another sector or research setting, this instrument (scale) also becomes “new”, since it is being tested (used) on a very different population / sample. So, you also need to perform EFA.

So, when should we use CFA? My point of view is that CFA should be used in empirical studies that use instruments (or scales) that have been tested in many previous studies (instruments or scales that have extensively being tested for their validity and reliability). Then, our only job is to confirm that these instruments (or scales) are valid and reliable in our research setting.

On a personal note, I tend to perform both analyses: first EFA, then CFA. I consider that the validity and reliability of my instrument is enhanced with this dual approach.

Dear all, thank you very much for your valuable insights.

Hi Deepani,

As explained by many already, it is better to perform both EFA and CFA.

Best wishes,

Bandini

Dear All, thank you very much for sharing your valuable thoughts and useful information.

If one of the dimensions of a variable in the model is the explored then can we skip the EFA to run the model on the SmartPLS 3?

Dear All,

I have a model in which the dependent variable is the innovation and the two other variables (items adapted). the factors or the dimension are three. The two dimensions have been adapted. However, the items of the third dimensions have been explored. I want to do the data analysis in the SmartPLS 3. 

As I have explored only the one of the three dimensions of the innovation; and I am sure that items of that the dimension do only belong to the innovation construct, therefore I conclude that factor structure is quite clear. Hence, there is no need to do EFA.

Is it correct? Could you provide me the reference to refer in this regard?

Waiting fir the kind response,

Best and the respectful regards, 

If one of the dimensions of a variable in the model is the.... Available from: https://www.researchgate.net/post/If_one_of_the_dimensions_of_a_variable_in_the_model_is_the_explored_then_can_we_skip_the_EFA_to_run_the_model_on_the_SmartPLS_3l [accessed Sep 3, 2017].

Excellent. Everybody however speaks CFA as being able to test which variables load onto the factor. I would like to test how certain participants/individual observations load onto the factors, with the notion that a factor may explain the variance in a group of participants more than the other. I would be even more interested in finding a sort of error term for each individual which shows how well the factor explains the data of that individual. I cannot seem to find a tested procedure for this. Any help would be much appreciated, in the mean time I will keep on exploring.

Cada uno de esos análisis (AFE y AFC) tiene su propio propósito, ninguno es mejor o más conveniente que otra, todo depende del propósito de la investigación. El exploratorio, lo utilizamos para configurar inicialmente que factores cargan más sobre un factor o constructo que deseamos evaluar. Es útil cuando estamos diseñando escalas de medición.

Por su parte, el análisis factorial confirmatorio permite determinar las cargas factoriales de las variables sobre el constructo que definen (variables que forman parte de las escalas de medición), y de esa manera validar, o confirmar, el modelo propuesto, y de alli la confirmación o no de las hipótesis planteadas alrededor de eso modelo. El confirmatorio nos permite también, a su vez, evaluar la fiabilidad de las escalas de medición diseñadas para cuantificar el modelo. Y como técnica base de un sistema de ecuaciones estructurales, permite estimar la bondad del ajuste de dicho modelo propuesto.

Actually, I find the terms confusing and misleading as well. In my experience, there is really only factor analysis (not CFA or EFA). In SPSS both CFA and EFA are performed using the same type of analysis so there is no difference in how you actually perform the analysis. The only difference is based on your expectations. Sometimes you may have a clear idea of the factors you will find. Other times you have no idea of how many factors will be identified and how these should be named. Sometimes it will be a mix of CFA and EFA. So, whether you are performing CFA or EFA is a matter of perspective, but the analysis itself is just factor analysis. I believe the confusion arises because we do not separate between the method (factor analysis) and the interpretation (confirmatory or exploratory).

Martin Brygger Andersen, please let me walk with you for a little while - largely because some time (years) ago I struggled with working out the difference between EFA (exploratory factor analysis) and CFA (confirmatory factor analysis).

At the time, I couldn't find anything about them that seemed to be clearly written and I didn't have access to a competent and tame statistician who could help me.

Actually, EFA and CFA are quite different things, and, furthermore, CFA cannot be performed in SPSS. (I wonder whether you might be confusing CFA with PCA, the latter being principal components analysis - which is available in SPSS, by default, though many statisticians regard as not being "true" factor analysis.)

I'm not sure how much more I could write at the moment that would be helpful, but the kind of "information" that is fed into an EFA is quite different from the kind of information that is fed into a CFA, and the output from each kind of analysis is substantially different.

Please let me know if you might find it helpful if I expanded my explanation(s).

Hey Robert Trevethan

I'm not entirely convinced as there is a degree of confusion on this subject. I know that factor analysis (FA) is often confused with Principal Component Analysis (PCA). In SPSS you find PCA under factor analysis, so I guess this adds to the confusion. I use Principal Axis Factoring (PAF) to conduct a proper factor analysis. In many books they regard PCA as factor analysis, even though this is not entirely true as the underlying math is different. However, PCA and PAF often yield almost the same results if the sample size is large. So whether one is conducting PCA or PAF, the results are often very similar. Mostly I perform factor analysis in SPSS to test models. If the model is validated I continue in AMOS and use structural equation modelling. When performing analysis in AMOS I create factors and connect indicators to them based on the results from the FA in SPSS. I would consider this CFA, as I try to confirm the existence of models known from previous theory and only make small alterations if necessary. If it was EFA, then I would work exploratory and inductively, right? So CFA is a deductive approach while EFA is an inductive approach? Or is this wrong? You are very welcome to share an article with me on the subject, if you know any? As far as I know, CFA and EFA are both performed with PAF in SPSS.

It looks like you were right Robert Trevethan

This link provides a small explanation. I always perform EFA first, before I do a CFA then :)

Martin Brygger Andersen, thanks for bouncing this around with me. I agree that having principal components analysis (PCA) as the default option (under Extraction) within Factor in SPSS can be confusing.

I also agree that, very often, much the same results come out whether researchers use PCA or some form of "genuine" factor analysis such as Principal Axis Factoring (PAF).

If you use AMOS, I think it should be said that, strictly speaking, you have moved away from SPSS, even though AMOS can be regarded as an add-on to SPSS. But I think it's important to realise that the output from EFA is quite different from that of CFA. With EFA, the output is likely to look like a set of columns with loadings on a particular number of factors (with the number of factors being either the SPSS default based on the number of eigenvalues greater than 1, or the number of factors that researchers set). Then it's possible to identify the variables that have sufficiently high and unique loadings within each column / factor. That's a simplified account, I know, but I think it is adequate for present purposes.

For CFA, the output is quite different and results from researchers specifying, in advance, exactly which variables they think are going to lie on exactly which factors. The output comprises such things as a chi-square value (with its degrees of freedom), a comparative fit index (CFI), a goodness-of-fit index (GFI), a Tucker-Lewis index (TLI), a root mean square error of approximation (RMSEA), and a standardised root mean square residual (SRMR) - and maybe more. Each of these metrics has a value (or limited range of values) that can be regarded as satisfactory. If the values produced by the CFA depart from those metrics' desirable criteria (sometimes the values from CFA output need to be higher than the criteria, sometimes lower), the structure being proposed by the researchers must be regarded as unsatisfactory - a failure.

It's a bit more complex than that, but I hope what I've written above is sufficiently helpful.

Certainly, playing around with EFA-type analyses to get a bit of confirmation for one's hunches may be helpful, but it isn't really a venture into confirmatory factor analysis.

Thanks for the website that you have provided above. I think it's good. However, in some ways it's quite a lot like what I had been reading some years ago. Because I didn't know what the difference between EFA and CFA was before I started reading the material back then, I wasn't able to absorb what those things were telling me. In other words, I needed to know what they were telling me BEFORE I read them so that I could then see what they were getting at.

I think one of the best ways to realise the difference between EFA and CFA is to see it in good research. Here's an example:

Ruan, J., Nie, Y., Hong, J., Monobe, G., Zheng, G., Kambara, H., & You, S. (2015). Cross-cultural validation of teachers’ sense of efficacy scale in three Asian countries: Test of measurement invariance. Journal of Psychoeducational Assessment, 33, 769–779. http://dx.doi.org/10.1177/0734282915574021

Or, perhaps better still, do a REAL confirmatory factor analysis oneself. :-)

I hope the above is helpful.

Excellent response, that makes a lot of sense to me. Confirmatory Factor Analysis is new to me, and I realize now that I have been given wrong information on the difference between EFA and CFA. I have learned that both EFA and CFA can be performed within SPSS. But confirmatory Factor Analysis is a different, and sometimes very complicated, beast, also when the sample size is huge. It is nearly impossible to a get a decent fit using either the chi-square test statistic or the chi-square/degrees of freedom statistic. It's good to know that the difference between EFA and CFA is more clear cut. Thanks for helping, Robert Trevethan

Martin Brygger Andersen, you're really welcome. I'm probably able to help primarily because I used to be in the same spot that you have been.

Chi-square is not a particularly good metric in CFA because it is influenced by sample size, so methodologists recommend dividing it by its degrees of freedom (which you've referred to above), with the result being referred to as the "normed chi-square". The normed chi-square, ideally should be less than 3 in a CFA, but some say that values between 3 and 5 are acceptable.

In my experience, whether a CFA is "successful" or not depends on a number of things, e.g., the number of items in an analysis, the number of proposed factors, and the strength of the loadings on the factors in an EFA.

One of the important aspects of all this is that EFA and CFA should not be conducted with the same set of data. Doing so is, in a sense, too "circular".

Because factor analysis is happiest when large participant numbers are involved, there is the unfortunate need to have a large number of participants if there is an intention to conduct both EFAs and CFAs.

Incidentally, I've been doing both EFAs and CFAs with colleagues recently. It's interesting to see what bubbles up - sometimes reassuring, sometimes disappointing.

All the best with your research - whatever you're using!

If you don't go for structural equation modeling then EFA is enough for you.

Personally, I think using an existing measurement in a different context in your case (population) should apply CFA unless the instrument is translated. EFA is only applicable to instruments that have not been used i.e., the instruments are new. Again it depends on the context of the study. Good luck.

I want to point out something which is foremost but was neither asked about by the questioner nor pointed by any other respondent- Pilot testing of the scale/items constituting the scale. If the scale already exists and there is a change in context, then obviously the researcher would like to adapt the questionnaire accordingly. The real question to ask is how much of change in context (geography, language of questionnaire, socio-demography of respondent, domain of research etc.) is happening. If not much is changing (eg. Using the scale to "measure the durability" of rubber tyres designed for 2 wheelers while being used for 4 wheelers), then just translate the scale items and do a pilot testing on ~50 samples and test for its internal consistency and validity. This will show the reliability of the scale, and omission of EFA is justifiable, and you can proceed directly to CFA. While, If the scale is a behavioral one, as in social sciences (eg. intention, purchase behavior, trust, satisfaction etc.) then the change in context is more impactful and it is recommended to perform a 2-step factor analysis i.e., EFA followed by CFA.

I hope it helps.

Great conversion. I had no idea about EFA and CFA. I am learning and want to perform myself for my upcoming DMSES questionnaire.