Analysis of multivariate frequency data by graphical models and generalizations of the multidimensional row-column association model

Models used to analyze cross-classifications of counts from psychological experiments must represent associations between multiple discrete variables and take into account attributes of stimuli, experimental conditions, or characteristics of subjects. The models must also lend themselves to psychological interpretations about underlying structures mediating the relationship between stimuli and responses. To meet these needs, the author extends the graphical latent variable models for nominal and/or ordinal data proposed by C. J. Anderson and J. K. Vermunt (2000) to situations in which dependencies between observed variables are not fully accounted for by the latent variables. The graphical models provide a unified framework for studying multivariate associations that include log-linear models and log-multiplicative association models as special cases.