Log Multiplicative Association Models for Multivariate Categorical Data with Latent Continuous Variable Interpretations

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The investigator makes connections between some recently developed models for categorical data and various existing models used in educational and psychological measurement. The observed relationships between variables is often postulated to be due to a small number of unobserved or latent variables. Frequently, the observed variables are discrete or are measured discretely (e.g., the response option selected on a multiple choice question or survey item, occupation, religion, highest degree earned). The investigator identifies equivalences between some more recently developed models for categorical data and existing latent variable models. The implications of these connections for the application and integration of these different models in social and behavioral science research, especially psychometric, will be examined. A second line of research that the investigator will undertake is in developing models that allow a researcher to incorporate (continuous and/or discretely measured) covariates into the models. This innovation will allow the association between categorical variables to be analyzed at the level of the individual, which permits tests of theories and hypotheses about underlying processes or mechanisms that give rise to observed relationships between discretely measured variables. The developments and innovations resulting from this work will expand the statistical tools available to social and behavioral science researchers in their investigations of the relationships between observed variables and theorized latent variables.