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.

scholarly journals Scale length does matter: Recommendations for Measurement Invariance Testing with Categorical Factor Analysis and Item Response Theory Approaches

2020 ◽  
Author(s):  
E. Damiano D'Urso ◽  
Kim De Roover ◽  
Jeroen K. Vermunt ◽  
Jesper Tijmstra
Keyword(s):  
Factor Analysis ◽  
Item Response Theory ◽  
Measurement Invariance ◽  
Item Response ◽  
Simulation Studies ◽  
Response Theory ◽  
Multiple Group ◽  
Item Level ◽  
Positive Rate ◽  
Scale Length

In social sciences, the study of group differences concerning latent constructs is ubiquitous. These constructs are generally measured by means of scales composed of ordinal items. In order to compare these constructs across groups, one crucial requirement is that they are measured equivalently or, in technical jargon, that measurement invariance holds across the groups. This study compared the performance of multiple group categorical confirmatory factor analysis (MG-CCFA) and multiple group item response theory (MG-IRT) in testing measurement invariance with ordinal data. A simulation study was conducted to compare the true positive rate (TPR) and false positive rate (FPR) both at the scale and at the item level for these two approaches under an invariance and a non-invariance scenario. The results of the simulation studies showed that the performance, in terms of the TPR, of MG-CCFA- and MG-IRT-based approaches mostly depends on the scale length. In fact, for long scales, the likelihood ratio test (LRT) approach, for MG-IRT, outperformed the other approaches, while, for short scales, MG-CCFA seemed to be generally preferable. In addition, the performance of MG-CCFA's fit measures, such as RMSEA and CFI, seemed to depend largely on the length of the scale, especially when MI was tested at the item level. General caution is recommended when using these measures, especially when MI is tested for each item individually. A decision flowchart, based on the results of the simulation studies, is provided to help summarizing the results and providing indications on which approach performed best and in which setting.

On Longitudinal Item Response Theory Models: A Didactic

2019 ◽  
Vol 45 (3) ◽  
pp. 339-368 ◽  
Author(s):  
Chun Wang ◽  
Steven W. Nydick
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Real Data ◽  
Measurement Model ◽  
Higher Order ◽  
Response Theory ◽  
Latent Growth ◽  
Multidimensional Irt ◽  
Irt Model ◽  
Irt Models

Recent work on measuring growth with categorical outcome variables has combined the item response theory (IRT) measurement model with the latent growth curve model and extended the assessment of growth to multidimensional IRT models and higher order IRT models. However, there is a lack of synthetic studies that clearly evaluate the strength and limitations of different multilevel IRT models for measuring growth. This study aims to introduce the various longitudinal IRT models, including the longitudinal unidimensional IRT model, longitudinal multidimensional IRT model, and longitudinal higher order IRT model, which cover a broad range of applications in education and social science. Following a comparison of the parameterizations, identification constraints, strengths, and weaknesses of the different models, a real data example is provided to illustrate the application of different longitudinal IRT models to model students’ growth trajectories on multiple latent abilities.

scholarly journals An Investigation of Chi-Square and Entropy Based Methods of Item-Fit Using Item Level Contamination in Item Response Theory

2020 ◽  
Vol 18 (2) ◽  
pp. 2-43
Author(s):  
William R. Dardick ◽  
Brandi A. Weiss
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Type I Error ◽  
Type I ◽  
Power Performance ◽  
Empirical Power ◽  
Response Theory ◽  
Chi Square ◽  
Item Fit ◽  
Item Level

New variants of entropy as measures of item-fit in item response theory are investigated. Monte Carlo simulation(s) examine aberrant conditions of item-level misfit to evaluate relative (compare EMRj, X2, G2, S-X2, and PV-Q1) and absolute (Type I error and empirical power) performance. EMRj has utility in discovering misfit.

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.

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.

A Bifactor Multidimensional Item Response Theory Model for Differential Item Functioning Analysis on Testlet-Based Items

2011 ◽  
Vol 35 (8) ◽  
pp. 604-622 ◽  
Author(s):  
Hirotaka Fukuhara ◽  
Akihito Kamata
Keyword(s):  
Item Response Theory ◽  
Differential Item Functioning ◽  
Item Response ◽  
Estimation Method ◽  
Multidimensional Item Response Theory ◽  
Multidimensional Item Response ◽  
Response Theory ◽  
Data Set ◽  
Detection Rates ◽  
Item Functioning

A differential item functioning (DIF) detection method for testlet-based data was proposed and evaluated in this study. The proposed DIF model is an extension of a bifactor multidimensional item response theory (MIRT) model for testlets. Unlike traditional item response theory (IRT) DIF models, the proposed model takes testlet effects into account, thus estimating DIF magnitude appropriately when a test is composed of testlets. A fully Bayesian estimation method was adopted for parameter estimation. The recovery of parameters was evaluated for the proposed DIF model. Simulation results revealed that the proposed bifactor MIRT DIF model produced better estimates of DIF magnitude and higher DIF detection rates than the traditional IRT DIF model for all simulation conditions. A real data analysis was also conducted by applying the proposed DIF model to a statewide reading assessment data set.

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.

scholarly journals Robustness of Projective IRT to Misspecification of the Underlying Multidimensional Model

2020 ◽  
Vol 44 (5) ◽  
pp. 362-375
Author(s):  
Tyler Strachan ◽  
Edward Ip ◽  
Yanyan Fu ◽  
Terry Ackerman ◽  
Shyh-Huei Chen ◽  
...  
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Real Data ◽  
Model Parameters ◽  
Simulation Studies ◽  
Response Theory ◽  
Computational Stability ◽  
Data Set ◽  
Response Data ◽  
Higher Dimensional

As a method to derive a “purified” measure along a dimension of interest from response data that are potentially multidimensional in nature, the projective item response theory (PIRT) approach requires first fitting a multidimensional item response theory (MIRT) model to the data before projecting onto a dimension of interest. This study aims to explore how accurate the PIRT results are when the estimated MIRT model is misspecified. Specifically, we focus on using a (potentially misspecified) two-dimensional (2D)-MIRT for projection because of its advantages, including interpretability, identifiability, and computational stability, over higher dimensional models. Two large simulation studies (I and II) were conducted. Both studies examined whether the fitting of a 2D-MIRT is sufficient to recover the PIRT parameters when multiple nuisance dimensions exist in the test items, which were generated, respectively, under compensatory MIRT and bifactor models. Various factors were manipulated, including sample size, test length, latent factor correlation, and number of nuisance dimensions. The results from simulation studies I and II showed that the PIRT was overall robust to a misspecified 2D-MIRT. Smaller third and fourth simulation studies were done to evaluate recovery of the PIRT model parameters when the correctly specified higher dimensional MIRT or bifactor model was fitted with the response data. In addition, a real data set was used to illustrate the robustness of PIRT.

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