Multinomial Restricted Unfolding for Multivariate Binary Data

Multivariate binary data with multiple binary response variables arise in many areas of research, including biology, psychology, medicine, dentistry, and other empirical sciences. In such data, the effect of a predictor on the response variable and the effect of a predictor on the association structure between the response variables is of interest. Multinomial Restricted Unfolding (MRU) is a probabilistic multidimensional unfolding model that can be used to analyse multicategory response variables in the presence of predictors. In this thesis, we investigated an extension of the MRU model to analyse multivariate binary data focusing on how diagnoses of depressive and anxiety disorders are influenced by personality traits and how the association between two disorders is affected by these personality traits. We compared the results using usual and squared Euclidean distances for the main effects and associations MRU models. We have demonstrated that MRU models using squared and usual...Show moreMultivariate binary data with multiple binary response variables arise in many areas of research, including biology, psychology, medicine, dentistry, and other empirical sciences. In such data, the effect of a predictor on the response variable and the effect of a predictor on the association structure between the response variables is of interest. Multinomial Restricted Unfolding (MRU) is a probabilistic multidimensional unfolding model that can be used to analyse multicategory response variables in the presence of predictors. In this thesis, we investigated an extension of the MRU model to analyse multivariate binary data focusing on how diagnoses of depressive and anxiety disorders are influenced by personality traits and how the association between two disorders is affected by these personality traits. We compared the results using usual and squared Euclidean distances for the main effects and associations MRU models. We have demonstrated that MRU models using squared and usual Euclidean distances can be used to analyse multivariate binary data, representing well the changes in log odds and the changes in log odds ratio. Our results indicated that the MRU models using squared Euclidean distances are more straightforward and easier to be interpreted than those using usual Euclidean distance. However, despite the more complicated interpretation, the model using the usual Euclidean distance is more flexible, which might lead to a better model fit. Regarding the change in log odds of having GAD, the main effects model results indicated a constant change in slope between different pairs of categories that represent GAD. For the associations model, the parallel lines indicate that the change in the slope was constant within a pair of categories that represents GAD but not the same for different pairs of categories. When usual Euclidean distances were used, the change in slope was not constant for both main effects and associations models. Regarding the interpretation rules to express the change in the log odds ratio, the main effects model showed that the association structure does not dependent on the value of the predictor variable. However, for the associations model, the log odds ratio is dependent on the value of the predictor variable, in which a constant change in slope is shown. When using usual Euclidean distances to explore the association structure between two response variables, the change in slope was not constant for both models.Show less

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Multinomial Restricted Unfolding for Multivariate Binary Data