  In a unidimensional factor model it is assumed that the set of indicators
that loads on this factor are conditionally independent given the latent
factor. Two indicators are, however, never conditionally independent given (a
set of) other indicators that load on this factor, as this would require one of
the indicators that is conditioned on to correlate one with the latent factor.
Although partial correlations between two indicators given the other indicators
can thus never equal zero (Holland and Rosenbaum, 1986), we show in this paper
that the partial correlations do need to be always weaker than the zero-order
correlations. More precisely, we prove that the partial correlation between two
observed variables that load on one factor given all other observed variables
that load on this factor, is always closer to zero than the zero-order
correlation between these two variables.
