On Fixed Marginal Distributions and Psychometric Network Models

This reply addresses the commentary by Epskamp et al. (in press) on our prior work, of using fixed marginals for sampling the data for testing hypothesis in psychometric network application. Mathematical results are presented for expected column (e.g., item prevalence) and row (e.g., subject severity) probabilities under three classical sampling schemes in categorical data analysis: (i) fixing the density, (ii) fixing either the row or column marginal, or (iii) fixing both the row and column marginal. It is argued that, while a unidimensional structure may not be the model we want, it is the structure we are confronted with given the binary nature of the data. Interpreting network models in the context of this artifactual structure is necessary, with preferred solutions to be expanding the item sets of disorders and moving away from the use of binary data and their associated constraints.