  This research concerns the estimation of latent linear or polychoric
correlations from fuzzy frequency tables. Fuzzy counts are of particular
interest to many disciplines including social and behavioral sciences, and are
especially relevant when observed data are classified using fuzzy categories -
as for socio-economic studies, clinical evaluations, content analysis,
inter-rater reliability analysis - or when imprecise observations are
classified into either precise or imprecise categories - as for the analysis of
ratings data or fuzzy coded variables. In these cases, the space of count
matrices is no longer defined over naturals and, consequently, the polychoric
estimator cannot be used to accurately estimate latent linear correlations. The
aim of this contribution is twofold. First, we illustrate a computational
procedure based on generalized natural numbers for computing fuzzy frequencies.
Second, we reformulate the problem of estimating latent linear correlations
from fuzzy counts in the context of Expectation-Maximization based maximum
likelihood estimation. A simulation study and two applications are used to
investigate the characteristics of the proposed method. Overall, the results
show that the fuzzy EM-based polychoric estimator is more efficient to deal
with imprecise count data as opposed to standard polychoric estimators that may
be used in this context.
