scholarly journals Fitting Logistic IRT Models: Small Wonder

1999 ◽  
Vol 2 ◽  
pp. 74-94 ◽  
Author(s):  
Miguel A. García-Pérez
Keyword(s):  
Item Response ◽  
State Of The Art ◽  
Logistic Function ◽  
Parameter Estimates ◽  
Data Set ◽  
Parameter Spaces ◽  
Irt Models ◽  
Best Fit ◽  
Logistic Functions ◽  
Metaphorical Interpretation

State-of-the-art item response theory (IRT) models use logistic functions exclusively as their item response functions (IRFs). Logistic functions meet the requirements that their range is the unit interval and that they are monotonically increasing, but they impose a parameter space whose dimensions can only be assigned a metaphorical interpretation in the context of testing. Applications of IRT models require obtaining the set of values for logistic function parameters that best fit an empirical data set. However, success in obtaining such set of values does not guarantee that the constructs they represent actually exist, for the adequacy of a model is not sustained by the possibility of estimating parameters. This article illustrates how mechanical adoption of off-the-shelf logistic functions as IRFs for IRT models can result in off-the-shelf parameter estimates and fits to data. The results of a simulation study are presented, which show that logistic IRT models can fit a set of data generated by IRFs other than logistic functions just as well as they fit logistic data, even though the response processes and parameter spaces involved in each case are substantially different. An explanation of why logistic functions work as they do is offered, the theoretical and practical consequences of their behavior are discussed, and a testable alternative to logistic IRFs is commented upon.

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 A General Unfolding IRT Model for Multiple Response Styles

2018 ◽  
Vol 43 (3) ◽  
pp. 195-210 ◽  
Author(s):  
Chen-Wei Liu ◽  
Wen-Chung Wang
Keyword(s):  
Response Style ◽  
Response Styles ◽  
Parameter Estimates ◽  
Data Set ◽  
Parameter Recovery ◽  
New Model ◽  
Irt Model ◽  
Irt Models ◽  
Strongly Agree ◽  
The Impact

It is commonly known that respondents exhibit different response styles when responding to Likert-type items. For example, some respondents tend to select the extreme categories (e.g., strongly disagree and strongly agree), whereas some tend to select the middle categories (e.g., disagree, neutral, and agree). Furthermore, some respondents tend to disagree with every item (e.g., strongly disagree and disagree), whereas others tend to agree with every item (e.g., agree and strongly agree). In such cases, fitting standard unfolding item response theory (IRT) models that assume no response style will yield a poor fit and biased parameter estimates. Although there have been attempts to develop dominance IRT models to accommodate the various response styles, such models are usually restricted to a specific response style and cannot be used for unfolding data. In this study, a general unfolding IRT model is proposed that can be combined with a softmax function to accommodate various response styles via scoring functions. The parameters of the new model can be estimated using Bayesian Markov chain Monte Carlo algorithms. An empirical data set is used for demonstration purposes, followed by simulation studies to assess the parameter recovery of the new model, as well as the consequences of ignoring the impact of response styles on parameter estimators by fitting standard unfolding IRT models. The results suggest the new model to exhibit good parameter recovery and seriously biased estimates when the response styles are ignored.

scholarly journals A study of alternative approaches to non-normal latent trait distributions in item response theory models used for health outcome measurement

2020 ◽  
Vol 29 (4) ◽  
pp. 1030-1048
Author(s):  
Niels Smits ◽  
Oğuzhan Öğreden ◽  
Mauricio Garnier-Villarreal ◽  
Caroline B Terwee ◽  
R Philip Chalmers
Keyword(s):  
Health Outcome ◽  
Item Response Theory ◽  
Health Outcomes ◽  
Item Response ◽  
Outcome Measurement ◽  
Latent Trait ◽  
Parameter Estimates ◽  
Response Theory ◽  
Zero Inflation ◽  
Irt Models

It is often unrealistic to assume normally distributed latent traits in the measurement of health outcomes. If normality is violated, the item response theory (IRT) models that are used to calibrate questionnaires may yield parameter estimates that are biased. Recently, IRT models were developed for dealing with specific deviations from normality, such as zero-inflation (“excess zeros”) and skewness. However, these models have not yet been evaluated under conditions representative of item bank development for health outcomes, characterized by a large number of polytomous items. A simulation study was performed to compare the bias in parameter estimates of the graded response model (GRM), polytomous extensions of the zero-inflated mixture IRT (ZIM-GRM), and Davidian Curve IRT (DC-GRM). In the case of zero-inflation, the GRM showed high bias overestimating discrimination parameters and yielding estimates of threshold parameters that were too high and too close to one another, while ZIM-GRM showed no bias. In the case of skewness, the GRM and DC-GRM showed little bias with the GRM showing slightly better results. Consequences for the development of health outcome measures are discussed.

scholarly journals irtplay: An R Package for Online Item Calibration, Scoring, Evaluation of Model Fit, and Useful Functions for Unidimensional IRT

2020 ◽  
Vol 44 (7-8) ◽  
pp. 563-565
Author(s):  
Hwanggyu Lim ◽  
Craig S. Wells
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
R Package ◽  
Model Fit ◽  
Parameter Estimates ◽  
Model Data ◽  
Polytomous Items ◽  
Item Calibration ◽  
Irt Model ◽  
Irt Models

The R package irtplay provides practical tools for unidimensional item response theory (IRT) models that conveniently enable users to conduct many analyses related to IRT. For example, the irtplay includes functions for calibrating online items, scoring test-takers’ proficiencies, evaluating IRT model-data fit, and importing item and/or proficiency parameter estimates from the output of popular IRT software. In addition, the irtplay package supports mixed-item formats consisting of dichotomous and polytomous items.

Item Response Theory and Music Testing

2019 ◽  
pp. 477-503
Author(s):  
Brian Wesolowski
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Test Scores ◽  
General Framework ◽  
Logistic Function ◽  
Response Theory ◽  
Measurement Models ◽  
Latent Constructs ◽  
Item Parameters ◽  
Introductory Overview

This chapter presents an introductory overview of concepts that underscore the general framework of item response theory. “Item response theory” is a broad umbrella term used to describe a family of mathematical measurement models that consider observed test scores to be a function of latent, unobservable constructs. Most musical constructs cannot be directly measured and are therefore unobservable. Musical constructs can therefore only be inferred based on secondary, observable behaviors. Item response theory uses observable behaviors as probabilistic distributions of responses as a logistic function of person and item parameters in order to define latent constructs. This chapter describes philosophical, theoretical, and applied perspectives of item response theory in the context of measuring musical behaviors.

scholarly journals Foveal Pit Morphology Characterization: A Quantitative Analysis of the Key Methodological Steps

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 699
Author(s):  
David Romero-Bascones ◽  
Maitane Barrenechea ◽  
Ane Murueta-Goyena ◽  
Marta Galdós ◽  
Juan Carlos Gómez-Esteban ◽  
...  
Keyword(s):  
State Of The Art ◽  
Parameter Estimates ◽  
Human Visual Perception ◽  
The Gaze ◽  
Center Location ◽  
Geometrical Features ◽  
Foveal Center ◽  
Location Methods ◽  
Morphology Characterization ◽  
Fitting Error

Disentangling the cellular anatomy that gives rise to human visual perception is one of the main challenges of ophthalmology. Of particular interest is the foveal pit, a concave depression located at the center of the retina that captures light from the gaze center. In recent years, there has been a growing interest in studying the morphology of the foveal pit by extracting geometrical features from optical coherence tomography (OCT) images. Despite this, research has devoted little attention to comparing existing approaches for two key methodological steps: the location of the foveal center and the mathematical modelling of the foveal pit. Building upon a dataset of 185 healthy subjects imaged twice, in the present paper the image alignment accuracy of four different foveal center location methods is studied in the first place. Secondly, state-of-the-art foveal pit mathematical models are compared in terms of fitting error, repeatability, and bias. The results indicate the importance of using a robust foveal center location method to align images. Moreover, we show that foveal pit models can improve the agreement between different acquisition protocols. Nevertheless, they can also introduce important biases in the parameter estimates that should be considered.

Construct validity of the Smoker Complaint Scale: A clinimetric analysis using Item Response Theory (IRT) models

2021 ◽  
Vol 117 ◽  
pp. 106849
Author(s):  
Danilo Carrozzino ◽  
Kaj Sparle Christensen ◽  
Giovanni Mansueto ◽  
Fiammetta Cosci
Keyword(s):  
Item Response Theory ◽  
Construct Validity ◽  
Item Response ◽  
Response Theory ◽  
Irt Models

scholarly journals A Benchmark and Evaluation of Non-Rigid Structure from Motion

2020 ◽  
Author(s):  
Sebastian Hoppe Nesgaard Jensen ◽  
Mads Emil Brix Doest ◽  
Henrik Aanæs ◽  
Alessio Del Bue
Keyword(s):  
Computer Vision ◽  
Structure From Motion ◽  
State Of The Art ◽  
The State ◽  
Quality Data ◽  
Data Set ◽  
Rigid Structure ◽  
Public Data ◽  
3D Information ◽  
Further Development

AbstractNon-rigid structure from motion (nrsfm), is a long standing and central problem in computer vision and its solution is necessary for obtaining 3D information from multiple images when the scene is dynamic. A main issue regarding the further development of this important computer vision topic, is the lack of high quality data sets. We here address this issue by presenting a data set created for this purpose, which is made publicly available, and considerably larger than the previous state of the art. To validate the applicability of this data set, and provide an investigation into the state of the art of nrsfm, including potential directions forward, we here present a benchmark and a scrupulous evaluation using this data set. This benchmark evaluates 18 different methods with available code that reasonably spans the state of the art in sparse nrsfm. This new public data set and evaluation protocol will provide benchmark tools for further development in this challenging field.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

Do firm characteristics of concentrated ownership firms affect dividend payout beyond traditional motivations?

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Avinash Jawade
Keyword(s):  
Agency Cost ◽  
Growth Potential ◽  
Firm Characteristics ◽  
Data Set ◽  
Holistic View ◽  
Dividend Payout ◽  
Content Type ◽  
Concentrated Ownership ◽  
Indian Context ◽  
Best Fit

Purpose This study aims to analyze the influence of firm characteristics in dividend payout in a concentrated ownership setting. Design/methodology/approach This study is probably the first to use the lasso technique for model selection and error prediction in the study of dividend payout in India. The lasso method comprises subsampling the available data set and performing reiterative regressions on those samples to generate the model with the best fit. This study incorporates four different ways of performing lasso treatment to get the best fit among them. Findings This study analyzes the influence of firm characteristics on dividend payout in the Indian context and asserts that firms with growth potential and earnings volatility do not hesitate to cut dividends. This study does not find evidence for signaling, agency cost and life cycle theories in a concentrated ownership setting. Earnings is the single most important factor to have a positive influence on dividend, while excessively leveraged firms are restrictive of dividend payout. Taxation has a prominent role in altering the way firms pay dividend. Research limitations/implications The recent changes in buyback taxation offer another opportunity to test the reactive behavior of firms. Also, given the disregard for traditional motivations, further research needs to be done to determine if dividend adjustments (on the lower side) help enhance firm value or not. Practical implications This study may help investors view dividends in a proper perspective. Firms give importance to investments over dividends and thus investors need not dwell on dividend changes if firms fulfill their growth potential. Social implications It lends perspective to investors about dividend changes and its importance. Originality/value The methodology used for analysis is absolutely original in the literature pertaining to dividend policy in the Indian context. The literature is abundant with theories advocating or opposing the eminence of dividend payout; however, this study takes a holistic view of all influential dividend determinants in literature to understand dividend payout.

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