Not very clear to me, what you did. Supposing you have two EFA, one for the expectations and one for the perceptions. Out of this you will have e (>1) factors for the expectations and p (>1) factors for the perceptions. now you want analyse the relation between e (independent / dependent ?) and p (independent / dependent ?) variables by a regression. This seems me not to be possible. Furthermore 22 cases and 25 variables at the end always is a tricky thing as this tends to create over-determined systems. What exactly is your model? 

Dear Thomas Sir,

Your assumption is right. I have done EFA on both Expectations-scale & Perceptions-scale separately. In fact, I am trying to measure tradeshows service quality, in Indian context. My questions are: Shall I completely depend on EFA done on P-scale? Any reference is available to ignore EFA on E-scale? Can I conduct regression analysis using factor scores, but how? Please understand, I have not yet built any model. Any reference material, you cite, certainly helps me build a model and formulate hypothesis for future testing. In case of regression analysis, please let me know which latent variable should be considered as DV. I agree with you that it is not possible to conduct CFA for this data (22 cases and 25 variables). But for EFA, I think even small sample is enough. Thank you for your time and response even my question lacks clarity.

Ok - maybe I now start to understand (or not) what you want to do: you used the same 25 variables to measure first (before visit?) the expectations and then (after visit?) the perception. And now you want to analyse what? A typical research question would be to find out to which extend in in which service dimensions expectations are fulfilled or not. Could you precise a bit more, what the research question is? What do you want to explain? 

My research objective is to assess quality of tradeshows service delivered by organisers as experienced by participating firms (22 responded). I have used Likert's 5-point scale to collect both expectations and perceptions on 25 service characteristics. The instrument was developed by me. Not tested earlier. I have factor analysed both E and P mean values to explore underlying factor structure. Bartlett's test is significant. I have read that regression analysis can be conducted after factor analysis. I am in a confused state of mind. Because the responses are original, I want to develop a new instrument for measuring tradeshows service quality. Am I required to conduct EFA second time with the reduced variables? or EFA once is enough? There is so much of confusion. I am struggling to decide. Please suggest me if there is any freeware available to analyse my data. Thank you for your concern.

First concerning EFA: it does not make sense to repeat it. A factor analysis creates out of partially dependent variables a reduced set of independent variables. If you make a factor analysis with independent variables you get as output the same variables again.

Concerning the question of measuring service quality I suggest to you to read the paper of Parasuraman, Zeithaml and Berry http://search.proquest.com/openview/7d007e04d78261295e5524f15bef6837/1?pq-origsite=gscholar&cbl=41988 which is one of the most common and well accepted method which can get applied to each type of service. 

Regression as a method in the most used cases as a concept tries to explain one dependent variable by m independent variables. But in your case you have a set of variables (and of course you can use the factors as variables) for expectations and for perceptions. No idea what is your hypothesis you have. 

Maybe an approach could be more to find out participating firms with similar expectation and perception profile. By this you would get a typology of the firms with different profiles / needs. And you would find out also types which currently have high expectations which perhaps are not fulfilled. This is something you can do with cluster analysis using either the original data or the factor scores - both is possible. 

Good luck!

Great understanding and also good suggestion regarding typology. I have another doubt. Because the factors extracted by me are the elements of the tradeshows service, can I conduct regression analysis by: i) combining all those factors and consider that blend as dependent variable, and ii) considering them separately as independent variables . Thank you Thomas Sir for your support.

If you consider using another software rather than Excel, then you can use R. Andy Field's Discovering Statistics using R provides step by step instructions for performing PCA in Chapter 17 (as well as regression in Ch. 7 and elsewhere for that matter). Dr. Revelle has authored the R library "psych" which performs EFA analyses as well (see links below).

Now regarding the essence of your question, I guess it boils down to what your research questions are. Do you expect a correlation between expectations and perceptions? Are you interested in the perceptions per se as an outcome? Or are you interested in another outcome for which you wish to examine the role of expectations and perceptions? Such questions are addressed with regression. For example:

P ~ E or P ~~ E (examine the degree to which perceptions depend on expectations)

P ~ E + X (examine the effect of another predictor X on P partialing out the effect of expectations)

Y ~ E + P + X (examine the unique effect of expectation, perceptions and another predictor X on a totally different outcome Y),

where ~ stands for regression, ~~ for correlation

On the other hand factor analysis will examine the structure of the perceptions and expectations. Is there a single underlying dimension or more? This question is addressed with any type of factor analysis. But the most critical question here is: Do you have reasons to believe that the factorial structure of expectations differs from the one of perceptions? Without knowing much about your research I daresay this seems implausible, even though I guess you can formally address the issue with CFA model comparison or perhaps other methods. Nonetheless, depending on the research question, as explained in the previous paragraph, it may make sense to first establish that the measurement model is the same before and after, and then address specific research questions with regression or other methods.

https://www.personality-project.org/r/r.guide.html

https://www.personality-project.org/r/book/