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UBC Theses and Dissertations

Ordinal generalizability theory using an underlying latent variable framework Ark, Tavinder K.


This dissertation introduces a method for estimating the variance components required in the use of generalizability theory (GT) with categorical ratings (e.g., ordinal variables). Traditionally, variance components in GT are estimated using statistical techniques that treat ordinal variables as continuous. This may lead to bias in the estimation of variance components and the resulting reliability coefficients (called G-coefficients). This dissertation demonstrates that variance components can be estimated using a structural equation modeling (SEM) technique called covariance structural modeling (CSM) of a polychoric or tetrachoric correlation matrix, which accounts for the metric of ordinal variables. The dissertation provides a proof of concept of this method, which will be called ordinal GT, using real data in the computation of a relative G-coefficient, and a simulation study presenting the relative merits of ordinal to conventional G-coefficients from ordinal data. The results demonstrate that ordinal GT is viable using CSM of the polychoric matrix of ordinal data. In addition, using a Monte Carlo simulation, the relative G-coefficients when ordinal data are naively treated as continuous are compared to when they are correctly treated as ordinal. The number of response categories, magnitude of the theoretical G-coefficient, and skewness of the item response distributions varied in experimental conditions for: (i) a two-facet crossed G-study design, and (ii) a one-facet partially nested G-study design. The results reveal that when ordinal data were treated as continuous, the empirical G-coefficients were consistently underestimates than their theoretical values. This was true regardless of the number of response categories, magnitude of the theoretical G-coefficient, and skewness. In contrast, the ordinal G-coefficients performed much better in all conditions. This dissertation shows that using CSM to model the polychoric correlation matrix provides better estimates of variance components in the GT of ordinal variables. It offers researchers a new statistical avenue for computing relative G-coefficients when using ordinal variables.

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