  Signal cancellation provides a radically new and efficient approach to
exploratory factor analysis, without matrix decomposition nor presetting the
required number of factors. Its current implementation requires that each
factor has at least two unique indicators. Its principle is that it is always
possible to combine two indicator variables exclusive to the same factor with
weights that cancel their common factor information. Successful combinations,
consisting of nose only, are recognized by their null correlations with all
remaining variables. The optimal combinations of multifactorial indicators,
though, typically retain correlations with some other variables. Their signal,
however, can be cancelled through combinations with unifactorial indicators of
their contributing factors. The loadings are estimated from the relative signal
cancellation weights of the variables involved along with their observed
correlations. The factor correlations are obtained from those of their
unifactorial indicators, corrected by their factor loadings. The method is
illustrated with synthetic data from a complex six-factor structure that even
includes two doublet factors. Another example using actual data documents that
signal cancellation can rival confirmatory factor analysis.
