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Power link functions in an ordinal regression model with Gaussian process priors

ENVIRONMETRICS 2019年第6期30卷 e2564-e2564页

作者： Li, D. Wang, X. Dey, D. K. Univ Southern Calif Keck Sch Med Alzheimers Therapeut Res Inst San Diego CA USA Univ Cincinnati Dept Math Sci Div Stat & Data Sci Cincinnati OH 45221 USA Univ Connecticut Dept Stat Storrs CT 06269 USA

Link functions and random effects structures are the two important components in building flexible regression models for dependent ordinal data. The power link functions include the commonly used links as special cases but have an additional skewness parameter, making the probability response curves adaptive to the data structure. It overcomes the arbitrary symmetry assumption imposed by the commonly used logistic or probit links as well as the fixed skewness in the complementary log-log or log-log links. By employing Gaussian processes, the regression model can incorporate various dependence structures in the data, such as temporal and spatial correlations. The full Bayesian estimation of the proposed model is conveniently implemented through RStan. Extensive simulation studies are carried out for discussion in model computation, parameterization, and evaluation in terms of estimation bias and overall model performance. The proposed model is applied to the PM2.5 data in Beijing and the Berberis thunbergii abundance data in New England. The results suggest that the proposed model leads to important improvement in estimation and prediction in modeling dependent ordinal response data.

关键词： Bayesian estimation Gaussian process ordinal regression model skewness

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Prediction of fabric handle value using ordinal regression model

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JOURNAL OF THE TEXTILE INSTITUTE 2015年第11期106卷 1161-1172页

作者： Sajjadi, Ali Sheikhzadeh, Mohammad Rikhtehgaran, Reyhaneh Hajrasouliha, Jalil Isfahan Univ Technol Dept Text Engn Esfahan Iran Isfahan Univ Technol Dept Math Sci Esfahan Iran

Bed sheet fabric as a kind of home textile has been used since many years ago. Bed sheet is very significant because of being in direct contact with body consecutively for a long period of time. Bed sheet surplus qualitative parameters such as fiber substance, method of printing, finishing, etc., have a significant parameter called handle. In this paper, we proceeded to consider the relationship between fabric handle as a qualitative parameter and physical parameters which influenced the fabric handle using statistical modeling. The statistical model used was ordinal regression model. The modeling was done by SPSS V. 19 software. We used 15 bed sheet fabrics. For subjective evaluation of 15 bed sheet fabrics, we selected 55 persons randomly as sample members according to Cochran's formula. Population was selected from senior BS students and MS students at Isfahan University of Technology (IUT). We asked persons to classify bed sheet fabrics based on their preference of fabric handle from 1 (lowest) to 5 (highest). Physical parameters values were obtained through standard experiments. Finally, we analyzed obtained data through SPSS V. 19 using ordinal regression model. Results showed a satisfying match between extracted data from the software and the real data from person's evaluation.

关键词： bed sheet fabric subjective evaluation handle value ordinal regression model SPSS

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Analyzing clustered continuous response variables with ordinal regression models

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BIOMETRICS 2023年第4期79卷 3764-3777页

作者： Tian, Yuqi Shepherd, Bryan E. E. Li, Chun Zeng, Donglin Schildcrout, Jonathan S. S. Vanderbilt Univ Dept Biostat Nashville TN 37203 USA Univ Southern Calif Dept Populat & Publ Hlth Sci Los Angeles CA USA Univ North Carolina Chapel Hill Dept Biostat Chapel Hill NC USA

Continuous response data are regularly transformed to meet regression modeling assumptions. However, approaches taken to identify the appropriate transformation can be ad hoc and can increase model uncertainty. Further, the resulting transformations often vary across studies leading to difficulties with synthesizing and interpreting results. When a continuous response variable is measured repeatedly within individuals or when continuous responses arise from clusters, analyses have the additional challenge caused by within-individual or within-cluster correlations. We extend a widely used ordinal regression model, the cumulative probability model (CPM), to fit clustered, continuous response data using generalized estimating equations for ordinal responses. With the proposed approach, estimates of marginal model parameters, cumulative distribution functions , expectations, and quantiles conditional on covariates can be obtained without pretransformation of the response data. While computational challenges arise with large numbers of distinct values of the continuous response variable, we propose feasible and computationally efficient approaches to fit CPMs under commonly used working correlation structures. We study finite sample operating characteristics of the estimators via simulation and illustrate their implementation with two data examples. One studies predictors of CD4:CD8 ratios in a cohort living with HIV, and the other investigates the association of a single nucleotide polymorphism and lung function decline in a cohort with early chronic obstructive pulmonary disease.

关键词： clustered data cumulative probability model generalized estimating equation longitudinal data ordinal regression model

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Reporting of regression models for ordinal Responses in Sports Sciences Field: A Systematic Review

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WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS 2025年第1期17卷

作者： Fernandez, Daniel Estopanan, Mireia Baumer, Benjamin Casals, Marti Univ Politecn Catalunya BarcelonaTech UPC Dept Stat & Operat Res DEIO Barcelona Spain Smith Coll Stat & Data Sci Northampton MA USA Univ Vic Cent Univ Catalonia UV UCC Fac Med Sport & Phys Act Studies Ctr CEEAF Barcelona Spain Univ Vic Cent Univ Catalonia UV UCC Sport Performance Anal Res Grp Barcelona Spain Univ Barcelona Natl Inst Phys Educ Catalonia INEFC Barcelona Spain

The integration of statistical methods in sports sciences has become essential for decision-making in performance analysis, injury prevention, and athlete outcomes. This work presents a systematic review following PRISMA guidelines to explore the application of ordinal regression models in the sports sciences field. A comprehensive search of articles published prior to March 4, 2023 identified 34 included studies. This search included widely recognized databases such as Web of Science, PubMed, and specialized journals of sports statistics, such as the Journal of Quantitative Analysis in Sports, and the Journal of Sports Analytics. The analysis reveals that 26.5% of these articles were published in statistics and sports statistics journals. Notably, R emerged as the primary software used for analysis in 38.8% of the studies. However, a significant majority (82.4%) of the studies did not provide data and code repositories. Among sports, soccer had the highest representation (28.6%), followed by basketball (17.1%). The most reported ordinal model was the proportional odds model (32.3%), followed by the mixed effects proportional odds model (11.8%), while a relevant proportion (29.4%) did not report the model used. Furthermore, 23.5% of articles proposed novel models. Validation tests for proportional odds models were not conducted in 53.3% of cases. This review underscores the importance of improved reporting practices, inclusivity in sport representation, and statistical education in advancing sports analytics.

关键词： ordinal regression model ordinal response sports sciences systematic review

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Addressing Multiple Detection Limits with Semiparametric Cumulative Probability models

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2024年第546期119卷 864-874页

作者： Tian, Yuqi Li, Chun Tu, Shengxin James, Nathan T. Harrell, FrankE. Shepherd, BryanE. Vanderbilt Univ Dept Biostat Nashville TN 37235 USA Univ Southern Calif Dept Populat & Publ Hlth Sci Los Angeles CA USA

Detection limits (DLs), where a variable cannot be measured outside of a certain range, are common in research. DLs may vary across study sites or over time. Most approaches to handling DLs in response variables implicitly make strong parametric assumptions on the distribution of data outside DLs. We propose a new approach to deal with multiple DLs based on a widely used ordinal regression model, the cumulative probability model (CPM). The CPM is a rank-based, semiparametric linear transformation model that can handle mixed distributions of continuous and discrete outcome variables. These features are key for analyzing data with DLs because while observations inside DLs are continuous, those outside DLs are censored and generally put into discrete categories. With a single lower DL, CPMs assign values below the DL as having the lowest rank. With multiple DLs, the CPM likelihood can be modified to appropriately distribute probability mass. We demonstrate the use of CPMs with DLs via simulations and a data example. This work is motivated by a study investigating factors associated with HIV viral load 6 months after starting antiretroviral therapy in Latin America;56% of observations are below lower DLs that vary across study sites and over time. Supplementary materials for this article are available online including a standardized description of the materials available for reproducing the work.

关键词： HIV Limit of detection ordinal regression model Transformation model

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How do individual characteristics, cognition, and environmental factors affect the beneficiaries' satisfaction of photovoltaic poverty alleviation projects?-Empirical evidence of 41 villages in rural China

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ENERGY FOR SUSTAINABLE DEVELOPMENT 2022年 66卷 271-286页

作者： Ding, Liping Dai, Qiyao He, Chenchen Zhang, Zumeng Shi, Yin China Univ Geosci Sch Econ & Management Wuhan 430074 Peoples R China China Univ Geosci Ctr Energy & Environm Management & Decis Making C Wuhan 430074 Peoples R China

As a substantial energy policy for poverty alleviation in China, photovoltaic poverty alleviation projects (PPAPs) have achieved a combination of poverty alleviation development, energy conservation and pollution emissions reduction. It is essential to explore how to improve the beneficiaries' satisfaction of the PPAPs, and thus to play a sustainable role in poverty alleviation. Based on the 1000 households' survey data collected in 41 poor villages in rural China. This paper explores the factors influencing beneficiaries' satisfaction using the entropy weight method (EWM), factor analysis, and ordinal regression model. The results indicate that:(1) there are some geographical differences in beneficiaries' satisfaction with PPAPs, and they are positively associated with the economic development performance of the poor areas;(2) beneficiaries' cognitive factors and environmental factors have disproportionate effects on the satisfaction, while the socio-demographic characteristics of beneficiaries have no significant influence on the comprehensive satisfaction. (C) 2022 International Energy Initiative. Published by Elsevier Inc. All rights reserved.

关键词： Photovoltaic poverty alleviation project Individual characteristics Cognition Environmental factors beneficiaries' satisfaction ordinal regression model

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Semiparametric Cumulative Probability models for Skewed, Censored, and Clustered Continuous Response Data

Semiparametric Cumulative Probability Models for Skewed, Cen...

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作者： Tian, Yuqi Vanderbilt University

学位级别：Ph.D., Doctor of Philosophy

Continuous response variables are often skewed and need to be transformed to meet modeling assumptions, but the choice of the transformation can be challenging. Censored and clustered continuous response data are also common in practice. We propose methods to address skewed, censored, and clustered continuous response data based on a semiparametric linear transformation model for ordinal responses, the cumulative probability model (CPM). First, via extensive simulations, we compare CPMs with a parametric transformation model, the most likely transformation model (MLT), for fitting continuous response data. Both approaches model cumulative distribution functions (CDFs) and require specifying a link function. With CPMs, the transformation is estimated nonparametrically by treating each continuous response as a distinct level. With MLTs, the transformation is parameterized using basis functions. Both methods have good performance. We apply them to an HIV biomarker study. Second, we propose new approaches based on CPMs to handle detection limits (DLs), where a variable is unable to be measured outside a certain range. Most approaches for DLs in response variables implicitly make parametric assumptions on distributions outside DLs. CPMs are rank-based and can handle mixed distributions of continuous and discrete response variables. While observations inside DLs are continuous, those outside DLs are generally put into discrete categories. With a single DL, CPMs assign values outside the DL as the lowest/highest rank. With multiple DLs, CPM likelihoods can be modified to distribute probability mass. We demonstrate our approaches with simulations and two HIV data examples. Finally, we extend CPMs to fit clustered continuous response variables based on generalized estimating equation methods for ordinal responses. With our approach, estimates of marginal parameters, CDFs, expectation, and quantiles conditional on covariates can be obtained without pre-transformation of the p

关键词： ordinal regression model Limit of detection Transformation model Clustered data

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Perceived pedestrian level of service in an urban central network: The case of a medium size Greek city

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CASE STUDIES ON TRANSPORT POLICY 2021年第2期9卷 889-905页

作者： Georgiou, Aggelos Skoufas, Anastasios Basbas, Socrates Aristotle Univ Thessaloniki Sch Rural & Surveying Engn Dept Transportat & Hydraul Engn Thessaloniki 54124 Greece

The assessment of pedestrian facilities largely depends on the Level of Service (LOS) calculation taking into account the effective width and the pedestrians' flows. This research focuses on the investigation of pedestrians' sociodemographic attributes (gender, age), qualitative components (perceived comfort) and the pedestrian streets' characteristics for LOS estimation as perceived by pedestrians. A questionnaire-based survey (including 200 interviewees) was carried out at the central pedestrianized network in the city of Ioannina, Greece. An ordinal regression model was developed based on the questionnaire' data. According to the findings females and elderly pedestrians tend to perceive lower LOS than males and younger pedestrians respectively. Furthermore, the level of perceived comfort in the impact area of the urban central network is an important determinant for the estimation of perceived LOS. These findings can be effectively utilized in the design of sustainable mobility policy recommendations and the promotion of active transport in an urban central area.

关键词： Level of service (LOS) Pedestrian street Walking ordinal regression model Sustainable urban mobility Active transport

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Perceived Pedestrian Level of Service: The case of Thessaloniki, Greece

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Transportation Research Procedia 2022年 60卷 124-131页

作者： Tiziana Campisi Giovanni Tesoriere Anastasios Skoufas Dimitris Zeglis Charilaos Andronis Socrates Basbas Faculty of Engineering and Architecture University of Enna KORE Cittadella Universitaria 94100 Enna Italy School of Architecture and the Built Environment KTH Royal Institute of Technology Stockholm Sweden School of Rural & Surveying Engineering Aristotle University of Thessaloniki 541 24 Thessaloniki Greece

Level of Service (LOS) is one of the most crucial components for the assessment of pedestrian facilities by mainly concerning the effective width as well as pedestrians’ flows. However, current research reveals that qualitative characteristics can also contribute to LOS estimation as perceived by pedestrians. Specifically, socio-demographic characteristics (i.e., age, gender) as well as characteristics related with perceived comfort and safety can be related with perceived LOS. A Revealed Preference (RP) face to face questionnaire-based survey (including 301 interviewees) was realized during October 2019 at a central pedestrian facility in the city of Thessaloniki, Greece. RP questionnaire survey assisted in gaining valuable knowledge concerning the factors that mainly affect pedestrians’ perceived LOS across the pedestrian facility. The examined pedestrian facility is one of the most important in Thessaloniki since it facilitates high pedestrian flows within the city center daily. The present survey considered pedestrians’ general mobility characteristics such as walking frequency along the facility and trip purpose. Additionally, the evaluation of the greater facility’ area in terms of land use attractiveness, comfort, personal and road safety, public transport, parking conditions and traffic delays, accessibility, pedestrians and bicycles were concerned as well. ordinal regression was the main tool for the development of the ordinal regression model, and therefore, for the conclusions’ drawing of the present research. The findings regarding perceived LOS can pave the way towards the design of sustainable policy concerning pedestrian facilities as well as the encouragement of active transport in urban areas.

关键词： Level of Service (LOS) pedestrian street walking ordinal regression model sustainable urban mobility active transport pedestrians

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An empirical comparison of two novel transformation models

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STATISTICS IN MEDICINE 2020年第5期39卷 562-576页

作者： Tian, Yuqi Hothorn, Torsten Li, Chun Harrell, Frank E., Jr. Shepherd, Bryan E. Vanderbilt Univ Dept Biostat Nashville TN 37203 USA Univ Zurich Inst Epidemiol Biostatist & Pravent Zurich Switzerland Case Western Reserve Univ Dept Populat & Quantitat Hlth Sci Cleveland OH 44106 USA

Continuous response variables are often transformed to meet modeling assumptions, but the choice of the transformation can be challenging. Two transformation models have recently been proposed: semiparametric cumulative probability models (CPMs) and parametric most likely transformation models (MLTs). Both approaches model the cumulative distribution function and require specifying a link function, which implicitly assumes that the responses follow a known distribution after some monotonic transformation. However, the two approaches estimate the transformation differently. With CPMs, an ordinal regression model is fit, which essentially treats each continuous response as a unique category and therefore nonparametrically estimates the transformation;CPMs are semiparametric linear transformation models. In contrast, with MLTs, the transformation is parameterized using flexible basis functions. Conditional expectations and quantiles are readily derived from both methods on the response variable's original scale. We compare the two methods with extensive simulations. We find that both methods generally have good performance with moderate and large sample sizes. MLTs slightly outperformed CPMs in small sample sizes under correct models. CPMs tended to be somewhat more robust to model misspecification and outcome rounding. Except in the simplest situations, both methods outperform basic transformation approaches commonly used in practice. We apply both methods to an HIV biomarker study.

关键词： HIV nonparametric maximum likelihood estimation ordinal regression model transformation model

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