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Alternative Approaches to Addressing Non-Normal Distributions in the Application of IRT Models to Personality Measures.

ABSTRACT: It is generally assumed that the latent trait is normally distributed in the population when estimating logistic item response theory (IRT) model parameters. This assumption requires that the latent trait be fully continuous and the population homogenous (i.e., not a mixture). When this normality assumption is violated, models are misspecified, and item and person parameter estimates are inaccurate. When normality cannot be assumed, it might be appropriate to consider alternative modeling approaches: (a) a zero-inflated mixture, (b) a log-logistic, (c) a Ramsay curve, or (d) a heteroskedastic-skew model. The first 2 models were developed to address modeling problems associated with so-called quasi-continuous or unipolar constructs, which apply only to a subset of the population, or are meaningful at one end of the continuum only. The second 2 models were developed to address non-normal latent trait distributions and violations of homogeneity of error variance, respectively. To introduce these alternative IRT models and illustrate their strengths and weaknesses, we performed real data application comparing results to those from a graded response model. We review both statistical and theoretical challenges in applying these models and choosing among them. Future applications of these and other alternative models (e.g., unfolding, diffusion) are needed to advance understanding about model choice in particular situations.

SUBMITTER: Reise SP

PROVIDER: S-EPMC6252010 | biostudies-literature | 2018 Jul-Aug

REPOSITORIES: biostudies-literature

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Alternative Approaches to Addressing Non-Normal Distributions in the Application of IRT Models to Personality Measures.

Reise Steven P SP Rodriguez Anthony A Spritzer Karen L KL Hays Ron D RD

Journal of personality assessment 20171031 4

It is generally assumed that the latent trait is normally distributed in the population when estimating logistic item response theory (IRT) model parameters. This assumption requires that the latent trait be fully continuous and the population homogenous (i.e., not a mixture). When this normality assumption is violated, models are misspecified, and item and person parameter estimates are inaccurate. When normality cannot be assumed, it might be appropriate to consider alternative modeling approa ...[more]

PMID: 29087217

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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

Alternative Approaches to Addressing Non-Normal Distributions in the Application of IRT Models to Personality Measures.

Publications

Alternative Approaches to Addressing Non-Normal Distributions in the Application of IRT Models to Personality Measures.

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