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16 pages, 476 KiB

Open AccessArticle

A Comparison of Limited Information Estimation Methods for the Two-Parameter Normal-Ogive Model with Locally Dependent Items

by Alexander Robitzsch

Stats 2024, 7(3), 576-591; https://doi.org/10.3390/stats7030035 - 21 Jun 2024

Cited by 1 | Viewed by 1202

Abstract

The two-parameter normal-ogive (2PNO) model is one of the most popular item response theory (IRT) models for analyzing dichotomous items. Consistent parameter estimation of the 2PNO model using marginal maximum likelihood estimation relies on the local independence assumption. However, the assumption of local [...] Read more.

The two-parameter normal-ogive (2PNO) model is one of the most popular item response theory (IRT) models for analyzing dichotomous items. Consistent parameter estimation of the 2PNO model using marginal maximum likelihood estimation relies on the local independence assumption. However, the assumption of local independence might be violated in practice. Likelihood-based estimation of the local dependence structure is often computationally demanding. Moreover, many IRT models that model local dependence do not have a marginal interpretation of item parameters. In this article, limited information estimation methods are reviewed that allow the convenient and straightforward handling of local dependence in estimating the 2PNO model. In detail, pairwise likelihood, weighted least squares, and normal-ogive harmonic analysis robust method (NOHARM) estimation are compared with marginal maximum likelihood estimation that ignores local dependence. A simulation study revealed that item parameters can be consistently estimated with limited information methods. At the same time, marginal maximum likelihood estimation resulted in biased item parameter estimates in the presence of local dependence. From a practical perspective, there were only minor differences regarding the statistical quality of item parameter estimates of the different estimation methods. Differences between the estimation methods are also compared for two empirical datasets. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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15 pages, 380 KiB

Open AccessArticle

On Underdispersed Count Kernels for Smoothing Probability Mass Functions

by Célestin C. Kokonendji, Sobom M. Somé, Youssef Esstafa and Marcelo Bourguignon

Stats 2023, 6(4), 1226-1240; https://doi.org/10.3390/stats6040076 - 4 Nov 2023

Cited by 2 | Viewed by 1903

Abstract

Only a few count smoothers are available for the widespread use of discrete associated kernel estimators, and their constructions lack systematic approaches. This paper proposes the mean dispersion technique for building count kernels. It is only applicable to count distributions that exhibit the [...] Read more.

Only a few count smoothers are available for the widespread use of discrete associated kernel estimators, and their constructions lack systematic approaches. This paper proposes the mean dispersion technique for building count kernels. It is only applicable to count distributions that exhibit the underdispersion property, which ensures the convergence of the corresponding estimators. In addition to the well-known binomial and recent CoM-Poisson kernels, we introduce two new ones such the double Poisson and gamma-count kernels. Despite the challenging problem of obtaining explicit expressions, these kernels effectively smooth densities. Their good performances are pointed out from both numerical and comparative analyses, particularly for small and moderate sample sizes. The optimal tuning parameter is here investigated by integrated squared errors. Also, the added advantage of faster computation times is really very interesting. Thus, the overall accuracy of two newly suggested kernels appears to be between the two old ones. Finally, an application including a tail probability estimation on a real count data and some concluding remarks are given. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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13 pages, 743 KiB

Open AccessArticle

Comparison between Two Algorithms for Computing the Weighted Generalized Affinity Coefficient in the Case of Interval Data

by Áurea Sousa, Osvaldo Silva, Leonor Bacelar-Nicolau, João Cabral and Helena Bacelar-Nicolau

Stats 2023, 6(4), 1082-1094; https://doi.org/10.3390/stats6040068 - 13 Oct 2023

Cited by 1 | Viewed by 1567

Abstract

From the affinity coefficient between two discrete probability distributions proposed by Matusita, Bacelar-Nicolau introduced the affinity coefficient in a cluster analysis context and extended it to different types of data, including for the case of complex and heterogeneous data within the scope of [...] Read more.

From the affinity coefficient between two discrete probability distributions proposed by Matusita, Bacelar-Nicolau introduced the affinity coefficient in a cluster analysis context and extended it to different types of data, including for the case of complex and heterogeneous data within the scope of symbolic data analysis (SDA). In this study, we refer to the most significant partitions obtained using the hierarchical cluster analysis (h.c.a.) of two well-known datasets that were taken from the literature on complex (symbolic) data analysis. h.c.a. is based on the weighted generalized affinity coefficient for the case of interval data and on probabilistic aggregation criteria from a VL parametric family. To calculate the values of this coefficient, two alternative algorithms were used and compared. Both algorithms were able to detect clusters of macrodata (aggregated data into groups of interest) that were consistent and consonant with those reported in the literature, but one performed better than the other in some specific cases. Moreover, both approaches allow for the treatment of large microdatabases (non-aggregated data) after their transformation into macrodata from the huge microdata. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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17 pages, 478 KiB

Open AccessArticle

Comparing Robust Linking and Regularized Estimation for Linking Two Groups in the 1PL and 2PL Models in the Presence of Sparse Uniform Differential Item Functioning

by Alexander Robitzsch

Stats 2023, 6(1), 192-208; https://doi.org/10.3390/stats6010012 - 25 Jan 2023

Cited by 7 | Viewed by 2516

Abstract

In the social sciences, the performance of two groups is frequently compared based on a cognitive test involving binary items. Item response models are often utilized for comparing the two groups. However, the presence of differential item functioning (DIF) can impact group comparisons. [...] Read more.

In the social sciences, the performance of two groups is frequently compared based on a cognitive test involving binary items. Item response models are often utilized for comparing the two groups. However, the presence of differential item functioning (DIF) can impact group comparisons. In order to avoid the biased estimation of groups, appropriate statistical methods for handling differential item functioning are required. This article compares the performance-regularized estimation and several robust linking approaches in three simulation studies that address the one-parameter logistic (1PL) and two-parameter logistic (2PL) models, respectively. It turned out that robust linking approaches are at least as effective as the regularized estimation approach in most of the conditions in the simulation studies. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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14 pages, 540 KiB

Open AccessArticle

Goodness-of-Fit and Generalized Estimating Equation Methods for Ordinal Responses Based on the Stereotype Model

by Daniel Fernández, Louise McMillan, Richard Arnold, Martin Spiess and Ivy Liu

Stats 2022, 5(2), 507-520; https://doi.org/10.3390/stats5020030 - 1 Jun 2022

Cited by 3 | Viewed by 3040

Abstract

Background: Data with ordinal categories occur in many diverse areas, but methodologies for modeling ordinal data lag severely behind equivalent methodologies for continuous data. There are advantages to using a model specifically developed for ordinal data, such as making fewer assumptions and [...] Read more.

Background: Data with ordinal categories occur in many diverse areas, but methodologies for modeling ordinal data lag severely behind equivalent methodologies for continuous data. There are advantages to using a model specifically developed for ordinal data, such as making fewer assumptions and having greater power for inference. Methods: The ordered stereotype model (OSM) is an ordinal regression model that is more flexible than the popular proportional odds ordinal model. The primary benefit of the OSM is that it uses numeric encoding of the ordinal response categories without assuming the categories are equally-spaced. Results: This article summarizes two recent advances in the OSM: (1) three novel tests to assess goodness-of-fit; (2) a new Generalized Estimating Equations approach to estimate the model for longitudinal studies. These methods use the new spacing of the ordinal categories indicated by the estimated score parameters of the OSM. Conclusions: The recent advances presented can be applied to several fields. We illustrate their use with the well-known arthritis clinical trial dataset. These advances fill a gap in methodologies available for ordinal responses and may be useful for practitioners in many applied fields. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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17 pages, 356 KiB

Open AccessArticle

Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data

by Chunling Wang and Xiaoyan Lin

Stats 2022, 5(2), 477-493; https://doi.org/10.3390/stats5020028 - 10 May 2022

Viewed by 2408

Abstract

Panel count data often occur in a long-term recurrent event study, where the exact occurrence time of the recurrent events is unknown, but only the occurrence count between any two adjacent observation time points is recorded. Most traditional methods only handle panel count [...] Read more.

Panel count data often occur in a long-term recurrent event study, where the exact occurrence time of the recurrent events is unknown, but only the occurrence count between any two adjacent observation time points is recorded. Most traditional methods only handle panel count data for a single type of event. In this paper, we propose a Bayesian semiparameteric approach to analyze panel count data for multiple types of events. For each type of recurrent event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by monotone I-splines. The correlation between multiple types of events is modeled by common frailty terms and scale parameters. Unlike many frequentist estimating equation methods, our approach is based on the observed likelihood and makes no assumption on the relationship between the recurrent process and the observation process. Under the Poisson counting process assumption, we develop an efficient Gibbs sampler based on novel data augmentation for the Markov chain Monte Carlo sampling. Simulation studies show good estimation performance of the baseline mean functions and the regression coefficients; meanwhile, the importance of including the scale parameter to flexibly accommodate the correlation between events is also demonstrated. Finally, a skin cancer data example is fully analyzed to illustrate the proposed methods. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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14 pages, 399 KiB

Open AccessArticle

ordinalbayes: Fitting Ordinal Bayesian Regression Models to High-Dimensional Data Using R

by Kellie J. Archer, Anna Eames Seffernick, Shuai Sun and Yiran Zhang

Stats 2022, 5(2), 371-384; https://doi.org/10.3390/stats5020021 - 15 Apr 2022

Cited by 2 | Viewed by 3075

Abstract

The stage of cancer is a discrete ordinal response that indicates the aggressiveness of disease and is often used by physicians to determine the type and intensity of treatment to be administered. For example, the FIGO stage in cervical cancer is based on [...] Read more.

The stage of cancer is a discrete ordinal response that indicates the aggressiveness of disease and is often used by physicians to determine the type and intensity of treatment to be administered. For example, the FIGO stage in cervical cancer is based on the size and depth of the tumor as well as the level of spread. It may be of clinical relevance to identify molecular features from high-throughput genomic assays that are associated with the stage of cervical cancer to elucidate pathways related to tumor aggressiveness, identify improved molecular features that may be useful for staging, and identify therapeutic targets. High-throughput RNA-Seq data and corresponding clinical data (including stage) for cervical cancer patients have been made available through The Cancer Genome Atlas Project (TCGA). We recently described penalized Bayesian ordinal response models that can be used for variable selection for over-parameterized datasets, such as the TCGA-CESC dataset. Herein, we describe our ordinalbayes R package, available from the Comprehensive R Archive Network (CRAN), which enhances the runjags R package by enabling users to easily fit cumulative logit models when the outcome is ordinal and the number of predictors exceeds the sample size,

P > N

, such as for TCGA and other high-throughput genomic data. We demonstrate the use of this package by applying it to the TCGA cervical cancer dataset. Our ordinalbayes package can be used to fit models to high-dimensional datasets, and it effectively performs variable selection. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

18 pages, 552 KiB

Open AccessArticle

A Flexible Mixed Model for Clustered Count Data

by Darcy Steeg Morris and Kimberly F. Sellers

Stats 2022, 5(1), 52-69; https://doi.org/10.3390/stats5010004 - 7 Jan 2022

Cited by 3 | Viewed by 4506

Abstract

Clustered count data are commonly modeled using Poisson regression with random effects to account for the correlation induced by clustering. The Poisson mixed model allows for overdispersion via the nature of the within-cluster correlation, however, departures from equi-dispersion may also exist due to [...] Read more.

Clustered count data are commonly modeled using Poisson regression with random effects to account for the correlation induced by clustering. The Poisson mixed model allows for overdispersion via the nature of the within-cluster correlation, however, departures from equi-dispersion may also exist due to the underlying count process mechanism. We study the cross-sectional COM-Poisson regression model—a generalized regression model for count data in light of data dispersion—together with random effects for analysis of clustered count data. We demonstrate model flexibility of the COM-Poisson random intercept model, including choice of the random effect distribution, via simulated and real data examples. We find that COM-Poisson mixed models provide comparable model fit to well-known mixed models for associated special cases of clustered discrete data, and result in improved model fit for data with intermediate levels of over- or underdispersion in the count mechanism. Accordingly, the proposed models are useful for capturing dispersion not consistent with commonly used statistical models, and also serve as a practical diagnostic tool. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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18 pages, 3927 KiB

Open AccessArticle

Smoothing in Ordinal Regression: An Application to Sensory Data

by Ejike R. Ugba, Daniel Mörlein and Jan Gertheiss

Stats 2021, 4(3), 616-633; https://doi.org/10.3390/stats4030037 - 21 Jul 2021

Cited by 4 | Viewed by 3416

Abstract

The so-called proportional odds assumption is popular in cumulative, ordinal regression. In practice, however, such an assumption is sometimes too restrictive. For instance, when modeling the perception of boar taint on an individual level, it turns out that, at least for some subjects, [...] Read more.

The so-called proportional odds assumption is popular in cumulative, ordinal regression. In practice, however, such an assumption is sometimes too restrictive. For instance, when modeling the perception of boar taint on an individual level, it turns out that, at least for some subjects, the effects of predictors (androstenone and skatole) vary between response categories. For more flexible modeling, we consider the use of a ‘smooth-effects-on-response penalty’ (SERP) as a connecting link between proportional and fully non-proportional odds models, assuming that parameters of the latter vary smoothly over response categories. The usefulness of SERP is further demonstrated through a simulation study. Besides flexible and accurate modeling, SERP also enables fitting of parameters in cases where the pure, unpenalized non-proportional odds model fails to converge. Full article

(This article belongs to the Special Issue Statistics, Analytics, and Inferences for Discrete Data)

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