A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories

2021 ◽  
pp. 107699862199255
Author(s):  
Roberto Colombi ◽  
Sabrina Giordano ◽  
Gerhard Tutz
Keyword(s):  
Item Response ◽  
Ethnic Minorities ◽  
Simulation Study ◽  
Rating Scale ◽  
Response Styles ◽  
Logit Models ◽  
Scale Mixture ◽  
Stochastic Orderings ◽  
Explanatory Variables ◽  
Proposed Model

A mixture of logit models is proposed that discriminates between responses to rating questions that are affected by a tendency to prefer middle or extremes of the scale regardless of the content of the item (response styles) and purely content-driven preferences. Explanatory variables are used to characterize the content-driven way of answering as well as the tendency to middle or extreme categories. The proposed model is extended to account for the presence of response styles in the case of several items, and the association among responses is described, both when they are content driven or dictated by response styles. In addition, stochastic orderings, related to the tendency to select middle or extreme categories, are introduced and investigated. A simulation study describes the effectiveness of the proposed model, and an application to a questionnaire on attitudes toward ethnic minorities illustrates the applicability of the modeling approach.

scholarly journals Item Response Tree Models to Investigate Acquiescence and Extreme Response Styles in Likert-Type Rating Scales

2019 ◽  
Vol 79 (5) ◽  
pp. 911-930 ◽  
Author(s):  
Minjeong Park ◽  
Amery D. Wu
Keyword(s):  
Item Response ◽  
Rating Scales ◽  
Rating Scale ◽  
Explanatory Models ◽  
Response Styles ◽  
Modeling Framework ◽  
Typical Application ◽  
Item Response Models ◽  
Extreme Response ◽  
Tree Models

Item response tree (IRTree) models are recently introduced as an approach to modeling response data from Likert-type rating scales. IRTree models are particularly useful to capture a variety of individuals’ behaviors involving in item responding. This study employed IRTree models to investigate response styles, which are individuals’ tendencies to prefer or avoid certain response categories in a rating scale. Specifically, we introduced two types of IRTree models, descriptive and explanatory models, perceived under a larger modeling framework, called explanatory item response models, proposed by De Boeck and Wilson. This extends the typical application of IRTree models for studying response styles. As a demonstration, we applied the descriptive and explanatory IRTree models to examine acquiescence and extreme response styles in Rosenberg’s Self-Esteem Scale. Our findings suggested the presence of two distinct extreme response styles and acquiescence response style in the scale.

scholarly journals Bayesian Analysis of a Quantile Multilevel Item Response Theory Model

2021 ◽  
Vol 11 ◽  
Author(s):  
Hongyue Zhu ◽  
Wei Gao ◽  
Xue Zhang
Keyword(s):  
Item Response Theory ◽  
Linear Regression ◽  
Item Response ◽  
Latent Variables ◽  
Structural Model ◽  
Theory Model ◽  
Response Theory ◽  
Explanatory Variables ◽  
Proposed Model ◽  
Multilevel Item Response Theory

Multilevel item response theory (MLIRT) models are used widely in educational and psychological research. This type of modeling has two or more levels, including an item response theory model as the measurement part and a linear-regression model as the structural part, the aim being to investigate the relation between explanatory variables and latent variables. However, the linear-regression structural model focuses on the relation between explanatory variables and latent variables, which is only from the perspective of the average tendency. When we need to explore the relationship between variables at various locations along the response distribution, quantile regression is more appropriate. To this end, a quantile-regression-type structural model named as the quantile MLIRT (Q-MLIRT) model is introduced under the MLIRT framework. The parameters of the proposed model are estimated using the Gibbs sampling algorithm, and comparison with the original (i.e., linear-regression-type) MLIRT model is conducted via a simulation study. The results show that the parameters of the Q-MLIRT model could be recovered well under different quantiles. Finally, a subset of data from PISA 2018 is analyzed to illustrate the application of the proposed model.

scholarly journals Estimating Parameters of Dichotomous and Ordinal Item Response Models with Gllamm

2007 ◽  
Vol 7 (3) ◽  
pp. 313-333 ◽  
Author(s):  
Xiaohui Zheng ◽  
Sophia Rabe-Hesketh
Keyword(s):  
Item Response ◽  
Latent Variable ◽  
Rating Scale ◽  
Ordinal Scale ◽  
Response Models ◽  
Item Response Models ◽  
Explanatory Variables ◽  
Test Items ◽  
Measurement Models ◽  
Latent Traits

Item response theory models are measurement models for categorical responses. Traditionally, the models are used in educational testing, where responses to test items can be viewed as indirect measures of latent ability. The test items are scored either dichotomously (correct–incorrect) or by using an ordinal scale (a grade from poor to excellent). Item response models also apply equally for measurement of other latent traits. Here we describe the one- and two-parameter logit models for dichotomous items, the partial-credit and rating scale models for ordinal items, and an extension of these models where the latent variable is regressed on explanatory variables. We show how these models can be expressed as generalized linear latent and mixed models and fitted by using the user-written command gllamm.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

Mokken Scale Analysis: Discussion and Application

2021 ◽  
Vol 8 (3) ◽  
pp. 672-695
Author(s):  
Thomas DeVaney
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Rating Scale ◽  
Scale Analysis ◽  
Guttman Scale ◽  
Response Theory ◽  
Data Set ◽  
Mokken Scale Analysis ◽  
Irt Models ◽  
Guttman Scaling

This article presents a discussion and illustration of Mokken scale analysis (MSA), a nonparametric form of item response theory (IRT), in relation to common IRT models such as Rasch and Guttman scaling. The procedure can be used for dichotomous and ordinal polytomous data commonly used with questionnaires. The assumptions of MSA are discussed as well as characteristics that differentiate a Mokken scale from a Guttman scale. MSA is illustrated using the mokken package with R Studio and a data set that included over 3,340 responses to a modified version of the Statistical Anxiety Rating Scale. Issues addressed in the illustration include monotonicity, scalability, and invariant ordering. The R script for the illustration is included.

scholarly journals Performance of Parametric Model for Line Transect Data

2020 ◽  
pp. 1-7
Author(s):  
Noryanti Muhammad ◽  
Gamil A.A. Saeed ◽  
Wan Nur Syahidah Wan Yusoff
Keyword(s):  
Simulation Study ◽  
Present Model ◽  
Parametric Model ◽  
Line Transect ◽  
Population Abundance ◽  
Line Transect Sampling ◽  
Detection Function ◽  
Transect Sampling ◽  
Proposed Model ◽  
Shoulder Condition

One of the most important sides of life is wildlife. There is growing research interest in monitoring wildlife. Line transect sampling is one of the techniques widely used for estimating the density of objects especially for animals and plants. In this research, a parametric estimator for estimation of the population abundance is developed. A new parametric model for perpendicular distances for detection function is utilised to develop the estimator. In this paper, the performance of the parametric model which was developed using a simulation study is presented. The detection function has non-increasing curve and a perfect probability at zero. Theoretically, the parametric model which has been developed is guar-anteed to satisfy the shoulder condition assumption. A simulation study is presented to validate the present model. Relative mean error (RME) and Relative Bias (RB) are used to compare the estimator with well-known existing estimators. The results of the simulation study are discussed, and the performance of the proposed model shows promising statistical properties which outperformed the existing models. Keywords: detection function, line transect data, parametric model

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