Although it depends on a few different aspects of the data, for an exploratory factor analysis, few hundred people is typically sufficient so 2,000 is definitely enough (see Osborne & Costello, 2004; MacCullum, Widaman, Zhang, & Hong, 1999; or Mundfrom, Shaw, & Ke, 2005).

For structural equation models, a classical rule of thumb is to have 5 or 10 observations for every parameter you are estimating in the model (see Gorusch 1983 or Everitt 1975), although these have been questioned in more recent studies. The complexity of the model (e.g., number of latent factors) has been found to be more important with more complex models needing larger samples. 

With a structural equation model, the main possible concern with a sample size of 2,000 may be that the minimum fit-fucntion chi-square statistic that tests model fit may be overpowered (it will say the model does not fit well when it actually might fit well). There is much debate about this is the statistical literature, but using approximate goodness of fit indices such as SRMR, RMSEA, and/or CFI may be preferable to the chi-square test to test model fit with a sample size that large. 

Achchuthan,

Perhaps you could find some use in my page:

https://www.researchgate.net/post/What_is_minimum_required_sample_size_to_compute_validity_for_questionnaires_scales2

Thanks for McNeish and Behzad Behzadnia

Dear ,

Daniel McNeish

Thanks for Your wonderful answer; further I have some doubt in my research study.

Research on Retail service quality and customer loyalty is being carried out presently by me.

Brief Description of the Study:

In our Scope, Retail Service Quality is considered as the independent variable. Further, it has five dimensions or Variables (Physical Aspects, Reliability, Personal Interaction, Problem Solving and Policy).

Meanwhile, Customer Loyalty is considered as the Dependent Variable.

I am confused on whether questions or items of both independent variable (Retail Service Quality) and Dependent Variable (Customer Loyalty) together can be factorized to get the unique construct through the Exploratory Factor Analysis?

Question No 02:

Researchers in the field of management and marketing suggested that, before performing the confirmatory factor analysis, exploratory factor analysis may be used to construct the unique model, which gives the real pathway to confirm the model via confirmatory factor analysis. Meanwhile, many researchers in the marketing field performed the confirmatory factor analysis with the questions or items of both the independent variable and dependent variable together to confirm the model.

Can questions or items of both independent variable (Retail Service Quality) and dependent variable (Customer Loyalty) together be factorized to get the unique construct through the Confirmatory Factor Analysis?

First on your question about sample size. This depends on many aspects. Indeed as Daniel McNeish mentioned, for every parameter you need about 10 independent cases. With independent I mean that observations from the same company are not independent. Same for observations within the same case over time. I say this, because I find your sample of 2000 rather large. Still, 2000 is not large if you have a factor model with 150 items. Actually, any analysis with 150 observed variables is bound to fail. For testing of factor models and the difficulties that can arise, e.g. the so-called oversensitivity of the CHI2-test, I advice to read my paper on the 'detection of misspecifications.

To your second question.It is considered a very bad idea if you use the same cases (data) to perform an EFA and then a CFA. My suggestion would be to confirm the scales using CFA, because someone else has already validated these scales. Moreover, please do not add all factors to your model at once. Try to start simple and then complicate your model step by step. You can also do CFA on dependent and independent at the same time. So, no EFA if you perform a CFA. However, I don't see any harm in only performing an EFA, especially if the factor analyses are only a necessary step to illustrate that the items can be used as a composite score. Don't get me wrong, I would prefer CFA, but only an EFA isn't bad either. 

Thank you sir, i need some justification from your Statement 

“ You can also do CFA on dependent and independent at the same time. So, no EFA if you perform a CFA.”

This means that, we can perform the CFA with dependent and independent variable.

But, we cant do like this procedure in EFA

Is it ok

In case of CFA or EFA, you can analyse the dependent and independent variables at the same time. 

My remark was about the fact that you should choose between CFA or EFA, because you cannot do both on the same sample, Thaat would be bad practice and a form of capitalization on chance.

PS. I. Cannot upload the publication because of copyright issues.

Thanks for your concern and answer 

I have 644 cases and two latent factors, authoritarian personality and populist attitude. Each of the two concepts I use is measured by three sub-factors, and everything is all right when it comes to numbers of cases. Thanks a lot boys who said that you need 10 cases for every parameter, I am still to learn what is a parameter.

Okay, 10 cases per parameter is a rule-of-thumb. However, it is really adviced not to push the limits, because in the end your estimates will become very unreliable. 

What is a parameter? It is difficult to imagine anyone who has received basic statistical training and who doesn't know what a parameter is. Nevertheless, a parameter is a factor loading, a variance, an effect, a correlation, a mean, an intercept, et cetera. So basically all the arrows and doeuble headed arrows, and more than that is a parameter.