Brian S. Everitt A Handbook of Statistical Analyses using SPSS

a) One-factor model
Goodness-of-fit Test
Chi-Square df Sig.
139.683 77 .000
b) Two-factor model
Goodness-of-fit Test
Chi-Square df Sig.
101.589 64 .002
a) Three-factor model
Goodness-of-fit Test
Chi-Square df Sig.
68.960 52 .058
Display 11.10 ML-based tests of model fit obtained for a series of factor models
for questionnaire variables.
We now employ principal factor analysis as our method for factor
extraction, i.e., fitting the factor analysis model by estimating factor
loadings and specific variances. Principal factor analysis is similar in many
respects to principal component analysis but uses what is sometimes
known as the reduced covariance or correlation matrix as the basis of the
calculations involved, i.e., the sample covariance or correlation matrix
with estimates of communalities on the main diagonal, where the communality
of a variable is the variance accountable for by the common
factors. One frequently used estimate of a variable’s communality is the
square of the multiple correlation of the variable with the other observed
variables. This is the method used in SPSS. From an initial version of the
reduced correlation or covariance matrix, factor loadings can be found
and these can then be used to update the communalities and so on until
some convergence criterion is satisfied (full details are given in Everitt
and Dunn, 2001).
The extraction method can be specified by the Method setting of the
Extraction sub-dialogue box (see Display 11.3); SPSS refers to principal
factor analysis as principal axis factoring. For principal factor analysis,
there is a choice between basing the analysis on the correlation or the
covariance matrix and we choose Covariance matrix. We also set the Number
of factors to 3 to fit a three-factor model and, finally, check Unrotated factor
solution so that the unrotated factor solution output will be given.
The resulting principal factor analysis output is shown in Display 11.11.
The “Communalities” table shows the communality estimates before and
© 2004 by Chapman & Hall/CRC Press LLC