scholarly journals RESIDUAL ANALYSIS IN RASCH POISSON COUNTS MODELS

2021 ◽  
Vol 39 (1) ◽  
pp. 206
Author(s):  
Naiara Caroline Aparecido dos SANTOS ◽  
Jorge Luiz BAZÁN
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Bayesian Approach ◽  
Residual Analysis ◽  
Model Parameters ◽  
Irt Model ◽  
Latent Traits ◽  
Over Time ◽  
Dichotomous Item ◽  
Poisson Counts

A Rasch Poisson counts (RPC) model is described to identify individual latent traits and facilities of the items of tests that model the error (or success) count in several tasks over time, instead of modeling the correct responses to items in a test as in the dichotomous item response theory (IRT) model. These types of tests can be more informative than traditional tests. To estimate the model parameters, we consider a Bayesian approach using the integrated nested Laplace approximation (INLA). We develop residual analysis to assess model t by introducing randomized quantile residuals for items. The data used to illustrate the method comes from 228 people who took a selective attention test. The test has 20 blocks (items), with a time limit of 15 seconds for each block. The results of the residual analysis of the RPC were promising and indicated that the studied attention data are not well tted by the RPC model.

scholarly journals The Impact of Markov Chain Convergence on Estimation of Mixture IRT Model Parameters

2020 ◽  
Vol 80 (5) ◽  
pp. 975-994
Author(s):  
Yoonsun Jang ◽  
Allan S. Cohen
Keyword(s):  
Markov Chain ◽  
Item Response Theory ◽  
Item Response ◽  
Monte Carlo Algorithm ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Response Theory ◽  
Irt Model ◽  
Mixture Irt ◽  
Item Response Theory Models

A nonconverged Markov chain can potentially lead to invalid inferences about model parameters. The purpose of this study was to assess the effect of a nonconverged Markov chain on the estimation of parameters for mixture item response theory models using a Markov chain Monte Carlo algorithm. A simulation study was conducted to investigate the accuracy of model parameters estimated with different degree of convergence. Results indicated the accuracy of the estimated model parameters for the mixture item response theory models decreased as the number of iterations of the Markov chain decreased. In particular, increasing the number of burn-in iterations resulted in more accurate estimation of mixture IRT model parameters. In addition, the different methods for monitoring convergence of a Markov chain resulted in different degrees of convergence despite almost identical accuracy of estimation.

Randomized Item Response Theory Models

2005 ◽  
Vol 30 (2) ◽  
pp. 189-212 ◽  
Author(s):  
Jean-Paul Fox
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Variables ◽  
Model Parameters ◽  
Randomized Response ◽  
Response Theory ◽  
Explanatory Variables ◽  
Irt Model ◽  
Cheating Behavior ◽  
Item Response Theory Models

The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by an item response theory (IRT) model. The RR technique links the observed item response with the true item response. Attitudes can be measured without knowing the true individual answers. This approach makes also a hierarchical analysis possible, with explanatory variables, given observed RR data. All model parameters can be estimated simultaneously using Markov chain Monte Carlo. The randomized item response technique was applied in a study on cheating behavior of students at a Dutch University. In this study, it is of interest if students’ cheating behavior differs across studies and if there are indicators that can explain differences in cheating behaviors.

scholarly journals Evaluation of Buss-Perry aggression Questionnaire with item response theory (IRT)

Psihologija ◽  
2012 ◽  
Vol 45 (2) ◽  
pp. 189-207 ◽  
Author(s):  
Bojana Dinic ◽  
Bojan Janicic
Keyword(s):  
Item Response Theory ◽  
Psychometric Properties ◽  
Item Response ◽  
Physical Aggression ◽  
Verbal Aggression ◽  
The Other ◽  
Irt Model ◽  
Graded Responses ◽  
Gender And Age ◽  
Aggression Questionnaire

The aim of this research was to examine the psychometric properties of the Buss-Perry Aggression Questionnaire on Serbian sample, using the IRT model for graded responses. AQ contains four subscales: Physical aggression, Verbal aggression, Hostility and Anger. The sample included 1272 participants, both gender and age ranged from 18 to 68 years, with average age of 31.39 (SD = 12.63) years. Results of IRT analysis suggested that the subscales had greater information in the range of above-average scores, namely in participants with higher level of aggressiveness. The exception was Hostilisty subscale, because it was informative in the wider range of trait. On the other hand, this subscale contains two items which violate assumption of homogenity. Implications for measurement of aggressiveness are discussed.

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 An item response theory analysis of an item pool for the recovering quality of life (ReQoL) measure

2020 ◽  
Author(s):  
Anju Devianee Keetharuth ◽  
Jakob Bue Bjorner ◽  
Michael Barkham ◽  
John Browne ◽  
Tim Croudace ◽  
...  
Keyword(s):  
Mental Health ◽  
Item Response Theory ◽  
Item Response ◽  
Measurement Precision ◽  
Model Parameters ◽  
Item Pool ◽  
Response Theory ◽  
Differential Item Function ◽  
Wide Range ◽  
Internal Construct Validity

Abstract Purpose ReQoL-10 and ReQoL-20 have been developed for use as outcome measures with individuals aged 16 and over, experiencing mental health difficulties. This paper reports modelling results from the item response theory (IRT) analyses that were used for item reduction. Methods From several stages of preparatory work including focus groups and a previous psychometric survey, a pool of items was developed. After confirming that the ReQoL item pool was sufficiently unidimensional for scoring, IRT model parameters were estimated using Samejima’s Graded Response Model (GRM). All 39 mental health items were evaluated with respect to item fit and differential item function regarding age, gender, ethnicity, and diagnosis. Scales were evaluated regarding overall measurement precision and known-groups validity (by care setting type and self-rating of overall mental health). Results The study recruited 4266 participants with a wide range of mental health diagnoses from multiple settings. The IRT parameters demonstrated excellent coverage of the latent construct with the centres of item information functions ranging from − 0.98 to 0.21 and with discrimination slope parameters from 1.4 to 3.6. We identified only two poorly fitting items and no evidence of differential item functioning of concern. Scales showed excellent measurement precision and known-groups validity. Conclusion The results from the IRT analyses confirm the robust structure properties and internal construct validity of the ReQoL instruments. The strong psychometric evidence generated guided item selection for the final versions of the ReQoL measures.

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.

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.

scholarly journals Item Response Theory Analyses of Barkley’s Adult Attention-Deficit/Hyperactivity Disorder Rating Scales

2020 ◽  
Vol 35 (7) ◽  
pp. 1094-1108
Author(s):  
Morgan E Nitta ◽  
Brooke E Magnus ◽  
Paul S Marshall ◽  
James B Hoelzle
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Adult Adhd ◽  
Rating Scales ◽  
Rating Scale ◽  
Self Report ◽  
Clinical Population ◽  
Response Theory ◽  
Item Level ◽  
Latent Traits

Abstract There are many challenges associated with assessment and diagnosis of ADHD in adulthood. Utilizing the graded response model (GRM) from item response theory (IRT), a comprehensive item-level analysis of adult ADHD rating scales in a clinical population was conducted with Barkley's Adult ADHD Rating Scale-IV, Self-Report of Current Symptoms (CSS), a self-report diagnostic checklist and a similar self-report measure quantifying retrospective report of childhood symptoms, Barkley's Adult ADHD Rating Scale-IV, Self-Report of Childhood Symptoms (BAARS-C). Differences in item functioning were also considered after identifying and excluding individuals with suspect effort. Items associated with symptoms of inattention (IA) and hyperactivity/impulsivity (H/I) are endorsed differently across the lifespan, and these data suggest that they vary in their relationship to the theoretical constructs of IA and H/I. Screening for sufficient effort did not meaningfully change item level functioning. The application IRT to direct item-to-symptom measures allows for a unique psychometric assessment of how the current DSM-5 symptoms represent latent traits of IA and H/I. Meeting a symptom threshold of five or more symptoms may be misleading. Closer attention given to specific symptoms in the context of the clinical interview and reported difficulties across domains may lead to more informed diagnosis.

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