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Analyzing rating distributions with heaps and censoring points using the generalized Craggit model.

ABSTRACT: In this article, we introduce a new, highly flexible model to analyze distributions with heaps and censoring points, which we call the generalized Craggit model. Distributions with heaps and censoring points can be found in many social science applications. For example, such distributions can be the result of sequential or multistep rating processes. Our model is a combination of a Craggit model and a generalized ordered probit model. It can account for multiple heaps and censoring points in distributions. We used this model to analyze a factorial survey experiment on earnings justice attitudes in the SOEP-Pretest 2008. In this experiment, a three-step rating instrument was used, which resulted in a rating distribution with heaps and censoring. Our generalized Craggit model fits the data of this experiment much better than a hierarchical linear model, which is the method that is usually implemented to analyze factorial survey experiments.

SUBMITTER: Lang V

PROVIDER: S-EPMC7155229 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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Analyzing rating distributions with heaps and censoring points using the generalized Craggit model.

Lang Volker V Groß Martin M

MethodsX 20200319

In this article, we introduce a new, highly flexible model to analyze distributions with heaps and censoring points, which we call the generalized Craggit model. Distributions with heaps and censoring points can be found in many social science applications. For example, such distributions can be the result of sequential or multistep rating processes. Our model is a combination of a Craggit model and a generalized ordered probit model. It can account for multiple heaps and censoring points in dis ...[more]

PMID: 32309151

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Project description:BACKGROUND:Volatile organic compounds (VOC), which include many hazardous chemicals, have been used extensively in personal, commercial and industrial products. Due to the variation in source emissions, differences in the settings and environmental conditions where exposures occur, and measurement issues, distributions of VOC concentrations can have multiple modes, heavy tails, and significant portions of data below the method detection limit (MDL). These issues challenge standard parametric distribution models needed to estimate the exposures, even after log-transformation of the data. METHODS:This paper considers mixture of distributions that can be directly applied to concentration and exposure data. Two types of mixture distributions are considered: the traditional finite mixture of normal distributions, and a semi-parametric Dirichlet process mixture (DPM) of normal distributions. Both methods are implemented for a sample data set obtained from the Relationship between Indoor, Outdoor and Personal Air (RIOPA) study. Performance is assessed based on goodness-of-fit criteria that compare the closeness of the density estimates with the empirical density based on data. The goodness-of-fit for the proposed density estimation methods are evaluated by a comprehensive simulation study. RESULTS:The finite mixture of normals and DPM of normals have superior performance when compared to the single normal distribution fitted to log-transformed exposure data. The advantages of using these mixture distributions are more pronounced when exposure data have heavy tails or a large fraction of data below the MDL. Distributions from the DPM provided slightly better fits than the finite mixture of normals. Additionally, the DPM method avoids certain convergence issues associated with the finite mixture of normals, and adaptively selects the number of components. CONCLUSIONS:Compared to the finite mixture of normals, DPM of normals has advantages by characterizing uncertainty around the number of components, and by providing a formal assessment of uncertainty for all model parameters through the posterior distribution. The method adapts to a spectrum of departures from standard model assumptions and provides robust estimates of the exposure density even under censoring due to MDL.

Dataset Information

Analyzing rating distributions with heaps and censoring points using the generalized Craggit model.

Publications

Analyzing rating distributions with heaps and censoring points using the generalized Craggit model.

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