  It is shown, with two sets of indicators that separately load on two distinct
factors, independent of one another conditional on the past, that if it is the
case that at least one of the factors causally affects the other, then, in many
settings, the process will converge to a factor model in which a single factor
will suffice to capture the covariance structure among the indicators. Factor
analysis with one wave of data can then not distinguish between factor models
with a single factor versus those with two factors that are causally related.
Therefore, unless causal relations between factors can be ruled out a priori,
alleged empirical evidence from one-wave factor analysis for a single factor
still leaves open the possibilities of a single factor or of two factors that
causally affect one another. The implications for interpreting the factor
structure of psychological scales, such as self-report scales for anxiety and
depression, or for happiness and purpose, are discussed. The results are
further illustrated through simulations to gain insight into the practical
implications of the results in more realistic settings prior to the convergence
of the processes. Some further generalizations to an arbitrary number of
underlying factors are noted.
