scholarly journals An Item Response Theory–Informed Strategy to Model Total Score Data from Composite Scales

2021 ◽  
Vol 23 (3) ◽  
Author(s):  
Gustaf J. Wellhagen ◽  
Sebastian Ueckert ◽  
Maria C. Kjellsson ◽  
Mats O. Karlsson
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Variable ◽  
Continuous Variable ◽  
Response Theory ◽  
Irt Models ◽  
Composite Scale ◽  
Level Data ◽  
Item Level ◽  
Scale Data

AbstractComposite scale data is widely used in many therapeutic areas and consists of several categorical questions/items that are usually summarized into a total score (TS). Such data is discrete and bounded by nature. The gold standard to analyse composite scale data is item response theory (IRT) models. However, IRT models require item-level data while sometimes only TS is available. This work investigates models for TS. When an IRT model exists, it can be used to derive the information as well as expected mean and variability of TS at any point, which can inform TS-analyses. We propose a new method: IRT-informed functions of expected values and standard deviation in TS-analyses. The most common models for TS-analyses are continuous variable (CV) models, while bounded integer (BI) models offer an alternative that respects scale boundaries and the nature of TS data. We investigate the method in CV and BI models on both simulated and real data. Both CV and BI models were improved in fit by IRT-informed disease progression, which allows modellers to precisely and accurately find the corresponding latent variable parameters, and IRT-informed SD, which allows deviations from homoscedasticity. The methodology provides a formal way to link IRT models and TS models, and to compare the relative information of different model types. Also, joint analyses of item-level data and TS data are made possible. Thus, IRT-informed functions can facilitate total score analysis and allow a quantitative analysis of relative merits of different analysis methods.

scholarly journals Latent Variable Modelling and Item Response Theory Analyses in Marketing Research

2016 ◽  
Vol 16 (2) ◽  
pp. 163-174 ◽  
Author(s):  
Justyna Brzezińska
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Variables ◽  
Latent Variable ◽  
Marketing Research ◽  
Response Theory ◽  
Irt Models ◽  
Latent Variable Modelling ◽  
Item Responses ◽  
Latent Traits

Abstract Item Response Theory (IRT) is a modern statistical method using latent variables designed to model the interaction between a subject’s ability and the item level stimuli (difficulty, guessing). Item responses are treated as the outcome (dependent) variables, and the examinee’s ability and the items’ characteristics are the latent predictor (independent) variables. IRT models the relationship between a respondent’s trait (ability, attitude) and the pattern of item responses. Thus, the estimation of individual latent traits can differ even for two individuals with the same total scores. IRT scores can yield additional benefits and this will be discussed in detail. In this paper theory and application with R software with the use of packages designed for modelling IRT will be presented.

scholarly journals Assessing Item-Level Fit for Higher Order Item Response Theory Models

2018 ◽  
Vol 42 (8) ◽  
pp. 644-659
Author(s):  
Xue Zhang ◽  
Chun Wang ◽  
Jian Tao
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Higher Order ◽  
Simulation Studies ◽  
Fit Indices ◽  
Response Theory ◽  
Chi Square ◽  
Detection Rates ◽  
Irt Models ◽  
Item Level

Testing item-level fit is important in scale development to guide item revision/deletion. Many item-level fit indices have been proposed in literature, yet none of them were directly applicable to an important family of models, namely, the higher order item response theory (HO-IRT) models. In this study, chi-square-based fit indices (i.e., Yen’s Q1, McKinley and Mill’s G2, Orlando and Thissen’s S-X2, and S-G2) were extended to HO-IRT models. Their performances are evaluated via simulation studies in terms of false positive rates and correct detection rates. The manipulated factors include test structure (i.e., test length and number of dimensions), sample size, level of correlations among dimensions, and the proportion of misfitting items. For misfitting items, the sources of misfit, including the misfitting item response functions, and misspecifying factor structures were also manipulated. The results from simulation studies demonstrate that the S-G2 is promising for higher order items.

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

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.

Clustering students according to their proficiency: a comparison between different approaches based on item response theory models

2021 ◽  
pp. 43-48
Author(s):  
Rosa Fabbricatore ◽  
Francesco Palumbo
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Clustering Algorithm ◽  
Latent Class ◽  
Latent Class Models ◽  
Response Theory ◽  
Homogeneous Groups ◽  
Final Grade ◽  
Irt Model ◽  
Irt Models

Evaluating learners' competencies is a crucial concern in education, and home and classroom structured tests represent an effective assessment tool. Structured tests consist of sets of items that can refer to several abilities or more than one topic. Several statistical approaches allow evaluating students considering the items in a multidimensional way, accounting for their structure. According to the evaluation's ending aim, the assessment process assigns a final grade to each student or clusters students in homogeneous groups according to their level of mastery and ability. The latter represents a helpful tool for developing tailored recommendations and remediations for each group. At this aim, latent class models represent a reference. In the item response theory (IRT) paradigm, the multidimensional latent class IRT models, releasing both the traditional constraints of unidimensionality and continuous nature of the latent trait, allow to detect sub-populations of homogeneous students according to their proficiency level also accounting for the multidimensional nature of their ability. Moreover, the semi-parametric formulation leads to several advantages in practice: It avoids normality assumptions that may not hold and reduces the computation demanding. This study compares the results of the multidimensional latent class IRT models with those obtained by a two-step procedure, which consists of firstly modeling a multidimensional IRT model to estimate students' ability and then applying a clustering algorithm to classify students accordingly. Regarding the latter, parametric and non-parametric approaches were considered. Data refer to the admission test for the degree course in psychology exploited in 2014 at the University of Naples Federico II. Students involved were N=944, and their ability dimensions were defined according to the domains assessed by the entrance exam, namely Humanities, Reading and Comprehension, Mathematics, Science, and English. In particular, a multidimensional two-parameter logistic IRT model for dichotomously-scored items was considered for students' ability estimation.

scholarly journals IRTBEMM: An R Package for Estimating IRT Models With Guessing or Slipping Parameters

2020 ◽  
Vol 44 (7-8) ◽  
pp. 566-567
Author(s):  
Shaoyang Guo ◽  
Chanjin Zheng ◽  
Justin L. Kern
Keyword(s):  
Maximum Likelihood ◽  
Item Response Theory ◽  
Item Response ◽  
R Package ◽  
Response Theory ◽  
Estimation Algorithms ◽  
Irt Models ◽  
Irt Estimation

A recently released R package IRTBEMM is presented in this article. This package puts together several new estimation algorithms (Bayesian EMM, Bayesian E3M, and their maximum likelihood versions) for the Item Response Theory (IRT) models with guessing and slipping parameters (e.g., 3PL, 4PL, 1PL-G, and 1PL-AG models). IRTBEMM should be of interest to the researchers in IRT estimation and applying IRT models with the guessing and slipping effects to real datasets.

Interval Estimation of Latent Variable Scores in Item Response Theory

2017 ◽  
Vol 43 (3) ◽  
pp. 259-285 ◽  
Author(s):  
Yang Liu ◽  
Ji Seung Yang
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Variable ◽  
Interval Estimation ◽  
Random Variable ◽  
Item Parameter ◽  
Response Theory ◽  
Inference Problem ◽  
Irt Model ◽  
Item Parameter Estimation

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a predictive inference problem: The target of prediction is a random variable that follows the true posterior of the LV conditional on the response pattern being scored. Various Bayesian, fiducial, and frequentist prediction intervals of LV scores, which can be obtained from a simple yet generic Monte Carlo recipe, are evaluated and contrasted via simulations based on several measures of prediction quality. An empirical data example is also presented to illustrate the use of candidate methods.

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