```Date: Fri, 4 May 2001 12:08:15 -0400 Reply-To: "Edgar F. Johns" Sender: "SPSSX(r) Discussion" From: "Edgar F. Johns" Subject: Re: How to select variables in a factor analysis Comments: To: Arthur J Kendall In-Reply-To: In evaluating the variables in an Exploratory Factor Analysis (EFA), I usually look at the Kaiser-Meyer-Olkin measure of sampling adequacy (MSA). Rather than a cut-off value of .5, Kaiser developed the following rule of thumb: <.5 = unacceptable; .5s = miserable; .6s = mediocre; .7s = middling, .8s = meritorious; .9s = marvelous (Dziuban & Shirkey, 1974).Consequently, if the overall value is less than .8, I'd consider it troubling. Dziuban & Shirkey also provide a formula for obtaining the MSA for individual variables. I also look at the final communality estimate (when using an iterative procedure for estimating communalities). If the final estimate is close to zero, you've got problems with that variable (at least with the current data and mix of other variables). What to do about it depends - you might drop it, retain it but request fewer factors to rotate, use an extraction method that doesn't use iteration to determine the communality estimates - on your situation and intent. Humphreys & Montanelli work produced the parallel analysis method for determining the number of factors to retain. In using this method, you need to calculate the eigenvalues from your correlation matrix with SMC's (squared multiple correlations) in the diagonal (and no iterations) and generate the scree from it. Hope this helps. Dziuban & Shirkey (1974). When is a correlation matrix appropriate for factor analysis? Some decision rules. Psychological Bulletin, 81, 358-361. Humphreys, & Montanelli. (1975). An investigation of the parallel analysis criterion for determining the number of common factors. Multivariate Behavioral Research, 19, 193-206. Montanelli & Humphreys (1976). Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A Monte Carlo study. Psychometrika, 41, 341-348. _____ Edgar F. Johns Obik, LLC 2906 River Meadow Circle Canton, MI 48188 Tel. 734.495.1292, Fax 734.495.1981 http://www.obik.com -----Original Message----- From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]On Behalf Of Arthur J Kendall Sent: Friday, May 04, 2001 8:57 AM To: SPSSX-L@LISTSERV.UGA.EDU Subject: Re: How to select variables in a factor analysis Sorry I don't have an exact citation. Montanelli and Humphreys in the 70's factored many sets of random numbers. They developed equations that input the number of cases, number of items, and factor number and output a predicted eigenvalue. Users could superimpose the curve from the predicted eigenvalues on the curve used in the scree test. They suggested retaining only the number of factors where the obtained eigenvalues were greater than those from the random data. I went back over a couple dozen factor analyses where several stopping rules were applied to ballpark the number of factors and interpretability determined the number to retain. In most cases, the number retained corresponded to (random eigenvalue + 1). This could be interpreted as 1 variable's more variance than would be obtained from random data. If I were doing a FA today I would still use the approach of using a series of stopping rules including M&H to ballbark the number to retain, but use interpretability for the final determination. >>> Chris Howden 05/04/01 12:46AM >>> Speaking of communalities it seems to me that a good PhD thesis would be to establish a test which evaluates if the amount of variance accounted for in a factor analysis could be attributed to chance, or if it is significant. Then only those variables that have a 'significant' amount of their variance explained would be retained in the factor model. This would allow a variable selection process similar to that used in multiple regression to be used in factor analysis. Christopher G Howden Environmental Statistician Dept Land & Water Conservation (Office) 02 9895 7130 (Mobile) 0410 689 945 ```

Back to: Top of message | Previous page | Main SPSSX-L page