Dear Heather,

If i understand you correctly, why do you need to conduct CFA on the established measure? This existing measure already had a known structure. All you need to worry about is the structure of your modified measure. Therefore, you can run CFA on the modified items to  check if your scale has the same structure as the original one.

Good luck.

If your new items replace the old ones, then you can apply the same CFA model from the original study and check whether the same structure holds. If, however, the instrument has been revised drastically (i.e., the content distribution of the items on the factors has changed), then you could begin with EFA and see the behaviors of those new items and whether they function similar to the old ones. If so, you can go ahead and fit your CFA model to confirm this. 

Dear Heather,

I am not sure how to understand the suggestions you have got so far. Although it might not be intended, but e.g. Okans suggestion leaves the impression, that you can first run EFA then CFA on the same data (and variables), which however would be strongly depreciated if not completely 'wrong' in the way of hypothesis testing is usually understood. So, I do not want to impute that this was his suggestion, but it just needs some clarification,  I think. A CFA must not run on the same dataset on which the EFA was applied on, and which therefore delivers the hypothesized factor structure.

However, coming back to your question. You say your goal is reducing sample size, or let's say in a more scientific way :), find the optimum required sample size.  By reading your questionI can not really follow how this relates to your methodological issues, but when I am asked to give a guess, then this one: the required sample size depends on factor identification and the explained item variances by the factors (communalities).

In MacCallum, Widaman, Zhang & Hong (1999). Sample size in factor analysis

you can find an answer to the question how to 'optimize' sample size. Basically, they suggest: when you have 3 items for each factor und average communailites higher than .7 then a sample size of 100 is sufficient, with medium communalities 200 would do it, and low communalities you should go with 400.

Considering this, I can only assume, that you want to improve the scales for making them more reliable, such that factors load higher on the new items (as reliability constrains the limits of the factor loadings and thus communalities too). In other words, you want to have scales (3 or 4 items each) in which the variances and covariances change (roughly speaking: because factors should explain more of the variances). Thus, CFA is not appropriate because there you fix the variance covariance structure. (Anyway, using new items requires EFA and afterwards validating the results with an additional data set on which you run a CFA).

Please let me know, when I got your goals wrong.

Hope this helps,

Best, René

There are two stages in research - Pilot Study and Field Study.

When you customize items or add new items to the existing one etc, you need to collect Pilot Study data and run EFA. The purpose here is to obtain the new combination of items measuring the said construct.Once you done with EFA, you need to collect field study data using the new combination of items. Using the field study data, you run CFA to validate the construct.

Because of estimation differences that are less relevant these days, EFA and CFA have grown up as quite distinct procedures. It sounds like you have a dataset and a model of how some of the relationships may be (so just want to find the values of these edges), are uncertain about the existence of other relations (so want to find these values but would count as zero if the data suggests that they are small), and have some which you will fix at zero. Am I characterizing this accurately? Sometimes the perceived schism between EFA and CFA is unhelpful.

I think, the best way would be to run a multigroup CFA (MGCFA) on both versions of the scale to test for measurement equivalence. This can easily be done via the semTools package in R, which is based on Lavaan. You will get information on how related the scales are in terms of the structure, error variances, intercepts and factor loadings. You can determine, if both scales yield identical values and can be directly compared (you need strict measurement equivalence for that).

We have just published an article about scale purification, i.e. the process of eliminating items from multi-item scales. We also discussed EFA and CFA. We have used the example of SCM, but our framework can be applied to any other discipline. Download: https://doi.org/10.1108/SCM-07-2016-0230 (or request via my ResearchGate page).