**Date:** Mon, 17 Oct 2005 08:57:05 -0400
**Reply-To:** Art@DrKendall.org
**Sender:** "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
**From:** Art Kendall <Art@DrKendall.org>
**Organization:** Social Research Consultants
**Subject:** Re: EFA and Sample Size
**In-Reply-To:** <01eb01c5d2ba$9c54a470$424b2144@ANDREAS>
**Content-Type:** text/plain; charset=windows-1250; format=flowed
Deciding how many factors to retain is very much an art. A lot depends
on the specifics of your situation.

What are you trying to accomplish with your dissertation?

How did you decide that there were eight constructs to be measured in
your model? Did previous work use the Kaiser criterion (1.00)?

Why promax? Why are you not interested in divergent validity of your
measure?

Why is it so difficult to get new cases? Is there a very limited
population you are studying? Are you getting a very high refusal rate?

The Kaiser criterion is roughly that "you certainly do not need to
extract factors that do not account for as much variance as an average
item".
You expect it to to yield "too many" factors.

To better guess what your situation is, you might hold your nose and
cross your fingers and try this.
Use a stopping rule of 8 factors with the data you have. Use (the scree
test) to ballpark the number of factors. Rotate that number of factors.
After rotation does the last factor have at least 4 items?.
Run parallel analysis (see the archives of this list). use increasing
numbers of cases until one of the original eigenvalues in the vicinity
of the scree exceeds that from random data by at least one.

Art
Art@DrKendall.org
Social Research Consultants
University Park, MD USA
(Inside the Washington, DC beltway.)
(301) 864-5570

Andreas N. Andreou wrote:

>Dear List,
>
>I have two questions about the adequacy of sample size in factor analysis and the extraction method. I am collecting data for my dissertation research and I am planning to use EFA with "Principal Axis Factoring" with "Promax" rotation. The number of factors to extract will be specified at 8 based on lit. review (not tested before). I want to use EFA to establish the factor structure to be later modeled in SEM using PLS.
>
>Sample size:
>My understanding from what I read is that there is no scientific rule on it but rather several rules of thump as listed below (:http://www2.chass.ncsu.edu/garson/pa765/factor.htm#cases):
> 1.. Rule of 10. There should be at least 10 cases for each item in the instrument being used.
> 2.. STV ratio. The subjects-to-variables ratio should be no lower than 5 (Bryant and Yarnold, 1995)
> 3.. Rule of 100: The number of subjects should be the larger of 5 times the number of variables, or 100. Even more subjects are needed when communalities are low and/or few variables load on each factor. (Hatcher, 1994)
> 4.. Rule of 150: Hutcheson and Sofroniou (1999) recommends at least 150 - 300 cases, more toward the 150 end when there are a few highly correlated variables, as would be the case when collapsing highly multicollinear variables.
> 5.. Rule of 200. There should be at least 200 cases, regardless of STV (Gorsuch, 1983)
> 6.. Rule of 300. There should be at least 300 cases (Norusis, 2005: 400).
> 7.. Significance rule. There should be 51 more cases than the number of variables, to support chi-square testing (Lawley and Maxwell, 1971)
>Question:
>1. I have 40 items in my questionnaire. How many cases do I need to be able to conduct EFA? I have been 4 months into data collection and I have collected 55 cases so far; I am expecting to reach 100 but not very optimistic in exceeding that by far.Is 100 cases enough?
>
>Extraction Method:
>2. When one specifies the number of factors in advance and when not? I have model with 8 factors (not tested before) and I want to see if that holds. I tried both extraction methods, when I pilot tested using the 55 cases and I am getting 2 more factors when using the eigenvalue >1 criterion.
>
>Thank you all for your answers,
>
>Regards,
>Andreas
>"Imagination is the destination; Knowledge is the journey"
>
>Andreas N. Andreou
>Doctoral Candidate & Research Assistant
>Institute for Knowledge and Innovation
>1776 G Street, NW Suite 101
>Washington, DC 20052
>Tel: 202-994-2951
>Fax: 202-994-0245
>E-Mail:aandreou@gwu.edu
>www.gwu.edu/~iki
>
>
>
>