A Kernel-Smoothed Version of SIBTEST With Applications to Local DIF Inference and Function Estimation

1996 ◽  
Vol 21 (4) ◽  
pp. 333-363 ◽  
Author(s):  
Jeffrey A. Douglas ◽  
William Stout ◽  
Louis V. DiBello
Keyword(s):  
Data Analysis ◽  
Item Response ◽  
Kernel Smoothing ◽  
Latent Trait ◽  
Real Data ◽  
Estimation Bias ◽  
Function Estimation ◽  
Item Response Function ◽  
And Function ◽  
Response Function Estimation

Smoothed SIBTEST, a nonparametric DIF detection procedure, amalgamates SIBTEST and kernel-smoothed item response function estimation. This procedure assesses DIF as a function of the latent trait θ that the test is designed to measure. Smoothed SIBTEST estimates this Junction with increased efficiency, as compared to SIBTEST, while providing hypothesis tests of local and global DIF. By means of kernel smoothing, smoothed SIBTEST reduces noise in local DIF estimation while retaining SIBTEST’s reduction of group-ability-difference-induced DIF estimation bias via use of regression-corrected estimates of ability as design points in the kernel smoothing. By contrast with most nonparametric procedures, matched examinee score cells are not needed, so sparse cell problems are avoided. The performance of smoothed SIBTEST is studied via simulation and real data analysis.

Nonparametric Item Response Function Estimates with the EM Algorithm

2002 ◽  
Vol 27 (3) ◽  
pp. 291-317 ◽  
Author(s):  
Natasha Rossi ◽  
Xiaohui Wang ◽  
James O. Ramsay
Keyword(s):  
Em Algorithm ◽  
Item Response ◽  
Functional Data ◽  
Latent Variable ◽  
Marginal Likelihood ◽  
Latent Trait ◽  
Functional Variation ◽  
The Em Algorithm ◽  
A New Technique ◽  
Item Response Function

The methods of functional data analysis are used to estimate item response functions (IRFs) nonparametrically. The EM algorithm is used to maximize the penalized marginal likelihood of the data. The penalty controls the smoothness of the estimated IRFs, and is chosen so that, as the penalty is increased, the estimates converge to shapes closely represented by the three-parameter logistic family. The one-dimensional latent trait model is recast as a problem of estimating a space curve or manifold, and, expressed in this way, the model no longer involves any latent constructs, and is invariant with respect to choice of latent variable. Some results from differential geometry are used to develop a data-anchored measure of ability and a new technique for assessing item discriminability. Functional data-analytic techniques are used to explore the functional variation in the estimated IRFs. Applications involving simulated and actual data are included.

Refinements of Stout’s Procedure for Assessing Latent Trait Unidimensionality

1993 ◽  
Vol 18 (1) ◽  
pp. 41-68 ◽  
Author(s):  
Ratna Nandakumar ◽  
William Stout
Keyword(s):  
Item Response ◽  
Latent Trait ◽  
Real Data ◽  
Data Sets ◽  
Simulation Studies ◽  
Nominal Level ◽  
Response Data ◽  
Latent Trait Model ◽  
Binary Item ◽  
Selection Of

This article provides a detailed investigation of Stout’s statistical procedure (the computer program DIMTEST) for testing the hypothesis that an essentially unidimensional latent trait model fits observed binary item response data from a psychological test. One finding was that DIMTEST may fail to perform as desired in the presence of guessing when coupled with many high-discriminating items. A revision of DIMTEST is proposed to overcome this limitation. Also, an automatic approach is devised to determine the size of the assessment subtests. Further, an adjustment is made on the estimated standard error of the statistic on which DIMTEST depends. These three refinements have led to an improved procedure that is shown in simulation studies to adhere closely to the nominal level of signficance while achieving considerably greater power. Finally, DIMTEST is validated on a selection of real data sets.

scholarly journals Nonparametric Item Response Models: A Comparison on Recovering True Scores

2020 ◽  
Author(s):  
Víthor Rosa Franco ◽  
Marie Wiberg
Keyword(s):  
Item Response ◽  
Kernel Smoothing ◽  
Real Data ◽  
Response Models ◽  
Item Response Models ◽  
Future Studies ◽  
Sum Scores ◽  
True Scores ◽  
Practical Implications ◽  
Nonparametric Item Response

Nonparametric procedures are used to add flexibility to models. Three nonparametric item response models have been proposed, but not directly compared: the Kernel smoothing (KS-IRT); the Davidian-Curve (DC-IRT); and the Bayesian semiparametric Rasch model (SP-Rasch). The main aim of the present study is to compare the performance of these procedures in recovering simulated true scores, using sum scores as benchmarks. The secondary aim is to compare their performances in terms of practical equivalence with real data. Overall, the results show that, apart from the DC-IRT, which is the model that performs the worse, all the other models give results quite similar to those when sum scores are used. These results are followed by a discussion with practical implications and recommendations for future studies.

Justifying the data analytical choice in single case research in relation to the expected data pattern

2019 ◽  
Author(s):  
Rumen Manolov
Keyword(s):  
Data Analysis ◽  
Visual Analysis ◽  
Multilevel Models ◽  
Single Case ◽  
Analytical Techniques ◽  
Real Data ◽  
Small Scale ◽  
Data User ◽  
Single Case Research ◽  
User Friendly

The lack of consensus regarding the most appropriate analytical techniques for single-case experimental designs data requires justifying the choice of any specific analytical option. The current text mentions some of the arguments, provided by methodologists and statisticians, in favor of several analytical techniques. Additionally, a small-scale literature review is performed in order to explore if and how applied researchers justify the analytical choices that they make. The review suggests that certain practices are not sufficiently explained. In order to improve the reporting regarding the data analytical decisions, it is proposed to choose and justify the data analytical approach prior to gathering the data. As a possible justification for data analysis plan, we propose using as a basis the expected the data pattern (specifically, the expectation about an improving baseline trend and about the immediate or progressive nature of the intervention effect). Although there are multiple alternatives for single-case data analysis, the current text focuses on visual analysis and multilevel models and illustrates an application of these analytical options with real data. User-friendly software is also developed.

scholarly journals Kernel methods in system identification, machine learning and function estimation: A survey

Automatica ◽  
2014 ◽  
Vol 50 (3) ◽  
pp. 657-682 ◽  
Author(s):  
Gianluigi Pillonetto ◽  
Francesco Dinuzzo ◽  
Tianshi Chen ◽  
Giuseppe De Nicolao ◽  
Lennart Ljung
Keyword(s):  
Machine Learning ◽  
System Identification ◽  
Kernel Methods ◽  
Function Estimation ◽  
And Function

Accuracy and sensitivity of different Bayesian methods for genomic prediction using simulation and real data

2020 ◽  
Vol 19 (3) ◽  
Author(s):  
Saheb Foroutaifar
Keyword(s):  
Data Analysis ◽  
Bayesian Methods ◽  
Milk Fat ◽  
Prediction Accuracy ◽  
Real Data ◽  
Fat Percentage ◽  
Real Data Analysis ◽  
Wide Range ◽  
High Heritability ◽  
Qtl Effects

AbstractThe main objectives of this study were to compare the prediction accuracy of different Bayesian methods for traits with a wide range of genetic architecture using simulation and real data and to assess the sensitivity of these methods to the violation of their assumptions. For the simulation study, different scenarios were implemented based on two traits with low or high heritability and different numbers of QTL and the distribution of their effects. For real data analysis, a German Holstein dataset for milk fat percentage, milk yield, and somatic cell score was used. The simulation results showed that, with the exception of the Bayes R, the other methods were sensitive to changes in the number of QTLs and distribution of QTL effects. Having a distribution of QTL effects, similar to what different Bayesian methods assume for estimating marker effects, did not improve their prediction accuracy. The Bayes B method gave higher or equal accuracy rather than the rest. The real data analysis showed that similar to scenarios with a large number of QTLs in the simulation, there was no difference between the accuracies of the different methods for any of the traits.

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.

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