Browsing by Author "Browne, Ryan P."
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Item Handling missing data in consumer hedonic tests arising from direct scaling(2016) Franczak, Brian C.; Castura, John C.; Browne, Ryan P.; Findlay, Christopher J.; McNicholas, Paul D.In sensory evaluation, it may be necessary to design experiments that yield incomplete data sets. As such, sensory scientists will need to utilize statistical methods capable of handling data sets with missing values. This article demonstrates the advantages of a model-based imputation procedure that simultaneously accounts for heterogeneity while imputing. We compare this model-based approach to the current state-of-the-art imputation procedures using two real data sets that arose from central location tests. These data sets contain missing values by design. In addition, these data sets have two data sets nested within each of them. We use these nested data sets to validate the results. Compared to the considered state-of-the-art imputation procedures, we find evidence that the model-based approach is able to recover the group structure and key characteristics of the data sets when a high percentage of the data are missing.Item A mixture of coalesced generalized hyperbolic distributions(2019) Tortora, Cristina; Franczak, Brian C.; Browne, Ryan P.; McNicholas, Paul D.A mixture of multiple scaled generalized hyperbolic distributions (MMSGHDs) is introduced. Then, a coalesced generalized hyperbolic distribution (CGHD) is developed by joining a generalized hyperbolic distribution with a multiple scaled generalized hyperbolic distribution. After detailing the development of the MMSGHDs, which arises via implementation of a multi-dimensional weight function, the density of the mixture of CGHDs is developed. A parameter estimation scheme is developed using the ever-expanding class of MM algorithms and the Bayesian information criterion is used for model selection. The issue of cluster convexity is examined and a special case of the MMSGHDs is developed that is guaranteed to have convex clusters. These approaches are illustrated and compared using simulated and real data. The identifiability of the MMSGHDs and the mixture of CGHDs are discussed in an appendix.Item Model-based clustering, classification, and discriminant analysis using the generalized hyperbolic distribution: MixGHD R package(2021) Tortora, Cristina; Browne, Ryan P.; ElSherbiny, Aisha; Franczak, Brian C.; McNicholas, Paul D.The MixGHD package for R performs model-based clustering, classification, and discriminant analysis using the generalized hyperbolic distribution (GHD). This approach is suitable for data that can be considered a realization of a (multivariate) continuous random variable. The GHD has the advantage of being flexible due to skewness, concentration, and index parameters; as such, clustering methods that use this distribution are capable of estimating clusters characterized by different shapes. The package provides five different models all based on the GHD, an efficient routine for discriminant analysis, and a function to measure cluster agreement. This paper is split into three parts: the first is devoted to the formulation of each method, extending them for classification and discriminant analysis applications, the second focuses on the algorithms, and the third shows the use of the package on real datasets. Software: GPL General Public License version 2 or version 3 or a GPL-compatible license.