scholarly journals Effectiveness of Person Fit Indices in Item Response Models with Different Degrees of Item Local Dependence

2020 ◽  
Vol 14 (1) ◽  
pp. 41
Author(s):  
Yaqoub Z. Al Shaqsy ◽  
Yousef A. Abu Shindi ◽  
Rashid S. Almehrizi
Keyword(s):  
Item Response ◽  
Item Difficulty ◽  
Standard Normal Distribution ◽  
Local Dependence ◽  
Fit Indices ◽  
Person Fit ◽  
Response Models ◽  
Item Response Models ◽  
Weighted Index ◽  
Distributional Properties

This study aimed to examine the effectiveness of person fit indices (Wright’s weighted index, Drasgow index and Almehrizi’s weighted index) in item response models with different degrees of item local dependence (0.0, 0.3, 0.6, and 0.9) using simulated item parameters. Item responses for 40 samples each with 10000 subjects (a total of 400000 subjects) were simulated on a test of 60 items. Item discrimination parameters ranged between 0.19 and 1.79 and item difficulty parameters ranged between -2 and +2. 20% of test items were manipulated to show local dependence for each level of local dependence degrees. Student ability was generated to follow a standard normal distribution. Assumptions of item response theory were examined in all data sets using exploratory factor analysis and residual analysis using NOHARM platform for unidimensionality and Q3 index for local independence. Results showed that there was an increase in the percentages of non-conforming persons when increasing the degree of items local dependence for the three person fit indices (Wright’s weighted index, Drasgow index and Almehrizi’s weighted index). Results showed also that the percentages of non-conforming persons were larger with Wright’s weighted index than with Drasgow index and Almehrizi’s weighted index. The distributional properties of the three indices showed relatively consistent in distributional properties. Drasgow index and Almehrizi’s weighted index were very similar distributional properties. Also, there was a larger agreement index between Wright’s weighted index and Drasgow index.

Item Response Models for Local Dependence Among Multiple Ratings

2014 ◽  
Vol 51 (3) ◽  
pp. 260-280 ◽  
Author(s):  
Wen-Chung Wang ◽  
Chi-Ming Su ◽  
Xue-Lan Qiu
Keyword(s):  
Item Response ◽  
Local Dependence ◽  
Response Models ◽  
Item Response Models

scholarly journals On the complementarity of classical test theory and item response models: item difficulty estimates and computerized adaptive testing

2015 ◽  
Vol 23 (88) ◽  
pp. 593-610
Author(s):  
Patrícia Costa ◽  
Maria Eugénia Ferrão
Keyword(s):  
Item Response ◽  
Computerized Adaptive Testing ◽  
Item Difficulty ◽  
Classical Test Theory ◽  
Adaptive Testing ◽  
Test Theory ◽  
Partial Credit Model ◽  
Response Models ◽  
Item Response Models ◽  
Classical Test

This study aims to provide statistical evidence of the complementarity between classical test theory and item response models for certain educational assessment purposes. Such complementarity might support, at a reduced cost, future development of innovative procedures for item calibration in adaptive testing. Classical test theory and the generalized partial credit model are applied to tests comprising multiple choice, short answer, completion, and open response items scored partially. Datasets are derived from the tests administered to the Portuguese population of students enrolled in the 4th and 6th grades. The results show a very strong association between the estimates of difficulty obtained from classical test theory and item response models, corroborating the statistical theory of mental testing.

scholarly journals Asymptotically Corrected Person Fit Statistics for Multidimensional Constructs with Simple Structure and Mixed Item Types

2020 ◽  
Author(s):  
Maxwell Hong ◽  
Lizhen Lin ◽  
Alison Cheng
Keyword(s):  
Item Response ◽  
Latent Trait ◽  
Standard Normal Distribution ◽  
Item Response Model ◽  
Person Fit ◽  
Item Response Models ◽  
Fit Statistics ◽  
Standard Normal ◽  
Work Done ◽  
Item Types

Person fit statistics are frequently used to detect deviating behavior when assuming an item response model generated the data. A common statistic, $l_z$, has been shown in previous studies to perform well under a myriad of conditions. However, it is well known that $l_z$ does not follow a standard normal distribution when using an estimated latent trait. As a result, corrections of $l_z$, called $l_z^*$, have been proposed in the literature for specific item response models. We propose a more general correction that is applicable to many types of data, namely survey or tests with multiple item types and underlying latent constructs, which subsumes previous work done by others. In addition, we provide corrections for multiple estimators of $\theta$, the latent trait, including MLE, MAP and WLE. We provide analytical derivations that justifies our proposed correction, as well as simulation studies to examine the performance of the proposed correction with finite test lengths. An applied example is also provided to demonstrate proof of concept. We conclude with recommendations for practitioners when the asymptotic correction works well under different conditions and also future directions.

scholarly journals Scale Alignment in the Between-Item Multidimensional Partial Credit Model

2021 ◽  
pp. 014662162110131
Author(s):  
Leah Feuerstahler ◽  
Mark Wilson
Keyword(s):  
Item Response ◽  
Kindergarten Readiness ◽  
Latent Trait ◽  
Individual Development ◽  
Partial Credit Model ◽  
Partial Credit ◽  
Response Models ◽  
Item Response Models ◽  
Item Parameters ◽  
Polytomous Item Response

In between-item multidimensional item response models, it is often desirable to compare individual latent trait estimates across dimensions. These comparisons are only justified if the model dimensions are scaled relative to each other. Traditionally, this scaling is done using approaches such as standardization—fixing the latent mean and standard deviation to 0 and 1 for all dimensions. However, approaches such as standardization do not guarantee that Rasch model properties hold across dimensions. Specifically, for between-item multidimensional Rasch family models, the unique ordering of items holds within dimensions, but not across dimensions. Previously, Feuerstahler and Wilson described the concept of scale alignment, which aims to enforce the unique ordering of items across dimensions by linearly transforming item parameters within dimensions. In this article, we extend the concept of scale alignment to the between-item multidimensional partial credit model and to models fit using incomplete data. We illustrate this method in the context of the Kindergarten Individual Development Survey (KIDS), a multidimensional survey of kindergarten readiness used in the state of Illinois. We also present simulation results that demonstrate the effectiveness of scale alignment in the context of polytomous item response models and missing data.

Stochastic Approximation Methods for Latent Regression Item Response Models

2010 ◽  
Vol 35 (2) ◽  
pp. 174-193 ◽  
Author(s):  
Matthias von Davier ◽  
Sandip Sinharay
Keyword(s):  
Item Response ◽  
Stochastic Approximation ◽  
Latent Variable ◽  
Reading Assessment ◽  
Mathematics Assessment ◽  
National Assessment ◽  
Variable Model ◽  
Response Models ◽  
Item Response Models ◽  
Latent Regression

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response theory (IRT) to a latent variable model with covariates serving as predictors of the conditional distribution of ability. Applications to estimating latent regression models for National Assessment of Educational Progress (NAEP) data from the 2000 Grade 4 mathematics assessment and the Grade 8 reading assessment from 2002 are presented and results of the proposed method are compared to results obtained using current operational procedures.

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