Students: Dissertation: Michael S. Johnson

Michael S. Johnson

ABSTRACT
Established methods for modeling multivariate systems described by categorical data include variable-based reconstructability analysis and log linear analysis. These methods are variable-based in the sense that the system constraint is described in terms of the variables comprising the system and any interactions among those variables. State-based modeling extends these established methods by permitting models defined in terms of system states, i.e., combinations of categories for subsets of the variables comprising the system.

If the constraint associated with a multivariate interaction is localized to just a few constituent cells, a state-based model can more precisely describe the nature of that constraint while using fewer parameters than a variable-based model. For confirmatory modeling this results in more powerful hypothesis tests.

In the context of exploratory modeling, state-based modeling greatly expands the lattice of possible system models both vertically, by enabling more granular changes in model complexity, and horizontally, by increasing the number of possible models at each level of complexity. Consequently, investigators have a much richer set of candidate models to consider, but also face challenges with respect to searching the model lattice efficiently and distinguishing real system structure from sampling artifacts.

This research establishes a conceptual framework for state-based reconstructability analysis, and provides computer software to support specification, fitting, and testing of state-based models. Problems of model estimation and the determination of model complexity are addressed. Simulation is used to compare state- and variable-based modeling with respect to sensitivity and specificity across a range of sample and effect sizes in a confirmatory analysis of an example system.

State-based modeling can also be applied in non-statistical settings. For example, in decision analysis, state-based modeling comprises an alternate technique for sensitivity analysis and, in some cases, simplification of event trees in which a utility measure is associated with each path. The results of such an analysis can provide a decision maker with insights regarding risk and opportunity that are not obtainable using variable-based techniques alone.

Friday, May 27, 2005
DISSERTATION COMMITTEE
Martin Zwick, Chair
Barry F. Anderson
James A. Paulson
Nancy A. Perrin
Roy W. Koch, Graduate Studies Rep.