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Open AccessFeature PaperArticle

A Definition of a Heywood Case in Item Response Theory Based on Fisher Information

by Jay Verkuilen and Peter J. Johnson

Entropy 2024, 26(12), 1096; https://doi.org/10.3390/e26121096 - 14 Dec 2024

Viewed by 1614

Heywood cases and other improper solutions occur frequently in latent variable models, e.g., factor analysis, item response theory, latent class analysis, multilevel models, or structural equation models, all of which are models with response variables taken from an exponential family. They have important consequences for scoring with the latent variable model and are indicative of issues in a model, such as poor identification or model misspecification. In the context of the 2PL and 3PL models in IRT, they are more frequently known as Guttman items and are identified by having a discrimination parameter that is deemed excessively large. Other IRT models, such as the newer asymmetric item response theory (AsymIRT) or polytomous IRT models often have parameters that are not easy to interpret directly, so scanning parameter estimates are not necessarily indicative of the presence of problematic values. The graphical examination of the IRF can be useful but is necessarily subjective and highly dependent on choices of graphical defaults. We propose using the derivatives of the IRF, item Fisher information functions, and our proposed Item Fraction of Total Information (IFTI) decomposition metric to bypass the parameters, allowing for the more concrete and consistent identification of Heywood cases. We illustrate the approach by using empirical examples by using AsymIRT and nominal response models. Full article

(This article belongs to the Special Issue Applications of Fisher Information in Sciences II)

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15 pages, 2467 KB

Open AccessArticle

Characteristics of Cyclist Crashes Using Polytomous Latent Class Analysis and Bias-Reduced Logistic Regression

by Yuta Sekiguchi, Masayoshi Tanishita and Daisuke Sunaga

Sustainability 2022, 14(9), 5497; https://doi.org/10.3390/su14095497 - 3 May 2022

Cited by 5 | Viewed by 2695

Abstract

Although the number of cyclist crashes is decreasing in Japan, the fatality rate is not. Thus, reducing their severity is a major challenge. We used a polytomous latent class analysis to understand their characteristics and bias-reduced logistic regression to analyze their severity. Specifically, 90,696 combinations and 139,955 cyclist accidents were divided into 17 classes. The variable contributing the most to the classification was the crash location. Common fatality risks included older age groups and rural areas, whereas other factors differed among crash locations. Median strips, stop signs, and boundaries between the sidewalk and roadway affected the severity of crashes at intersections. Moreover, the existence of a median strip, collision partner, and time period affected the severity of crashes between intersections. On the sidewalks, the fatality risk was higher when the front part of the bicycle was subjected to the collision. Full article

(This article belongs to the Special Issue Challenges and Strategies for Sustainable Transportation and Traffic Safety)

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19 pages, 362 KB

Open AccessArticle

Measurement of Inter-Individual Variability in Assessing the Quality of Life in Respondents with Celiac Disease

by Silvia Bacci, Daniela Caso, Rosa Fabbricatore and Maria Iannario

Psych 2020, 2(4), 296-314; https://doi.org/10.3390/psych2040023 - 23 Nov 2020

Viewed by 3175

Abstract

Quality of life of Celiac Disease (CD) patients is affected by constraints in their physical, social and emotional behaviour. Our objective is to assess differences in two relevant dimensions of the Celiac Quality of Life (CQoL) scale, Limitations due to the disease and Dysphoria (i.e., feelings of depression and discomfort), in relation to the perceived social support and some individual and disease-related characteristics. The paper exploits suitable unidimensional Item Response Theory (IRT) models to individually analyse the two mentioned dimensions of the CQoL and Multidimensional Latent Class IRT models for ordinal polytomous items in order to detect sub-populations of CD patients that are homogenous with respect to the perceived CQoL. The latter methods allow to address patients with similar characteristics to the same treatment, performing at the same time a more tailored overture to health promotion programmes. The analysis extracts the relevant patterns and relations among CD patients, disentangling respondents receiving CD diagnosis in adolescence or adult age rather than in childhood (the first perceive high levels of Limitations and Dysphoria), patients with high perceived social support, a factor influencing in a positive way motivation to engage in management of CD-related distress and psychological well-being, and participants who are married or cohabiting. The latter report higher latent trait levels. Full article

(This article belongs to the Special Issue Learning from Psychometric Data)

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24 pages, 489 KB

Open AccessArticle

Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data

by Alexander Robitzsch

J. Intell. 2020, 8(3), 30; https://doi.org/10.3390/jintelligence8030030 - 14 Aug 2020

Cited by 9 | Viewed by 5041

Abstract

The last series of Raven’s standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization for RLCMs is proposed. For polytomous item responses, different alternative fused regularization penalties are presented. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes. In total, three out of five latent classes are ordered for all items. For the remaining two classes, violations for two and three items were found, respectively, which can be interpreted as a kind of latent differential item functioning. Full article

(This article belongs to the Special Issue Analysis of an Intelligence Dataset)

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