What determines if GOF test is displayed for factor analysis?

[Bruce Weaver]

This one has me scratching my head a bit.  

Background:  I'm trying to replicate an example of exploratory factor analysis (EFA) with missing data from the UCLA website (see link below).  My syntax is shown below.  As you'll see, when I use maximum likelihood (ML) as the extraction method, I see a goodness-of-fit (GOF) test in the output when I extract 3 factors, but not when I extract 4 factors.  Apart from the number of factors to extract (and the presence of a /PLOT sub-command), the syntax is identical.  

Thus far, I've not found anything in the FM (or via Google) that explains why the GOF test does not always appear when one uses ML extraction.  Can anyone explain what's going on here?  

Cheers,
Bruce


* The Stata example can be seen here:
* http://www.ats.ucla.edu/stat/stata/faq/factor_missing.htm .

* The active dataset is a matrix dataset of EM correlations
* that were generated via MVA with /EM sub-command.

* Run a 4-factor model with ML + Varimax, as on the website.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /PLOT = Eigen
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(4) ITERATE(25) DELTA(0)
  /EXTRACTION ML
  /ROTATION VARIMAX
  /METHOD=CORRELATION.

* This is not a great model--the Scree plot suggests 3 factors.
* Run 3-factor model with ML extraction & Varimax rotation.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(3) ITERATE(25) DELTA(0)
  /EXTRACTION ML
  /ROTATION VARIMAX
  /METHOD=CORRELATION.

* The only changes I made to the first FACTOR command were
* 1) I deleted the /PLOT sub-command, and 2) I changed the
* number of factors to extract from 4 to 3.  Having made
* only those changes, I now see a Goodness-of-Fit (GOF) test
* that was not present in the results for the 4-factor model.

* Try again with 3 factors and an oblique rotation (OBLIMIN).

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(3) ITERATE(25) DELTA(0)
  /EXTRACTION ML
  /ROTATION OBLIMIN
  /METHOD=CORRELATION.

* GOF test still appears in the output.

* Back to 4-factor model, but with OBLIMIN.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(4) ITERATE(25) DELTA(0)
  /EXTRACTION ML
  /ROTATION OBLIMIN
  /METHOD=CORRELATION.

* No GOF test with 4-factor solution.

* Try 3-factor solution with PAF and OBLIMIN.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(3) ITERATE(25) DELTA(0)
  /EXTRACTION PAF
  /ROTATION OBLIMIN
  /METHOD=CORRELATION.

* No GOF test with PAF extraction and 3-factor solution.


p.s. - A 4-factor model with orthogonal rotation doesn't make much sense for this dataset (IMO)--but I ran it anyway so I could check the SPSS results against the Stata results shown on that webpage.  And FWIW, the solutions agreed very closely.  

[Johannes Herrmann]

Bruce,
I replicated what you described and the first EFA (code below) did not converge. Increasing the numbers of iterations did solve the problem, convergence was reached and the GOF test was displayed now.
In the EFA output, the is a small notice below the Factor Matrix table, if the extraction does not converge.

*No convergence, no GOF:.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /PLOT = Eigen
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(4) ITERATE(25) DELTA(0)
  /EXTRACTION ML
  /ROTATION VARIMAX
  /METHOD=CORRELATION.

*Convergence and GOF:.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /PLOT = Eigen
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(4) ITERATE(2500) DELTA(0)
  /EXTRACTION ML
  /ROTATION VARIMAX
  /METHOD=CORRELATION.

HTH,
Johannes

[Bruce Weaver]

Aha!  Thank you, Johannes--danke.  I had not noticed that warning.  Increasing the number of iterations fixes it.  

Cheers,
Bruce

Johannes Herrmann wrote

Bruce,
I replicated what you described and the first EFA (code below) did not converge. Increasing the numbers of iterations did solve the problem, convergence was reached and the GOF test was displayed now.
In the EFA output, the is a small notice below the Factor Matrix table, if the extraction does not converge.

*No convergence, no GOF:.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /PLOT = Eigen
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(4) ITERATE(25) DELTA(0)
  /EXTRACTION ML
  /ROTATION VARIMAX
  /METHOD=CORRELATION.

*Convergence and GOF:.

FACTOR MATRIX IN(COR=*)
  /MISSING LISTWISE
  /ANALYSIS = item13 to item28
  /PRINT INITIAL EXTRACTION ROTATION FSCORE
  /PLOT = Eigen
  /FORMAT BLANK(.3)
  /CRITERIA FACTORS(4) ITERATE(2500) DELTA(0)
  /EXTRACTION ML
  /ROTATION VARIMAX
  /METHOD=CORRELATION.

HTH,
Johannes