  The case that the factor model does not account for all the covariances of
the observed variables is considered. This is a quite realistic condition
because some model error as well as some sampling error should usually occur
with empirical data. It is shown that principal components representing
covariances not accounted for by the factors of the model can have a non-zero
correlation with the common factors of the factor model. Non-zero correlations
of components representing variance not accounted for by the factor model with
common factors were also found in a simulation study. Based on these results it
should be concluded that common factors can be correlated with variance
components representing model error as well as sampling error. In consequence,
even when researchers decide not to represent some small or trivial variance by
means of a common factor, these excluded variances can still be part of the
model.
