A comparison of parameter covariance estimation methods for item response models in an expectation-maximization framework

Pritikin, Joshua N.

doi:10.1080/23311908.2017.1279435

Cited by 14 publications

(26 citation statements)

References 21 publications

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“…Another advantage of the OIA with respect to the S-EM algorithm in particular is that reestimation of the model to obtain sufficiently close MLEs, or to obtain a better-behaved EM iteration history, is not required; hence, there will be no issues related to non-convergence when building the numerical Jacobian. As was highlighted in the simulation work presented by Pritikin (2017), non-convergence is a common occurrence with the S-EM algorithm, particularly for models with a larger number of estimated parameters from nonexponential families. When non-convergence does occur, the quality of the entire ACOV matrix must be called into question because the inversion of a poorly approximated observed-data information matrix will result in unpredictably distorted, and potentially misleading, ACOV estimates.…”

Section: Advantages Of the Oakes' Identity Approximationmentioning

confidence: 97%

“…Before beginning, it should be noted that this paper is not the first body of work to investigate a finite‐difference approach for Oakes's identity. To the best of the author's knowledge, Pritikin () was the first to apply a numerical estimate of Oakes's identity to multi‐parameter IRT models (Embretson & Reise, ; Lord & Novick, ) by using a simple forward difference approximation. Overall, Pritikin demonstrated the potential superiority of this numerical approximation in terms of computational efficiency and relative precision compared to techniques in current use for four multidimensional IRT models.…”

Section: Introductionmentioning

confidence: 99%

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Numerical approximation of the observed information matrix with Oakes' identity

Chalmers

2018

Brit J Math & Statis

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An efficient and accurate numerical approximation methodology useful for obtaining the observed information matrix and subsequent asymptotic covariance matrix when fitting models with the EM algorithm is presented. The numerical approximation approach is compared to existing algorithms intended for the same purpose, and the computational benefits and accuracy of this new approach are highlighted. Instructive and real-world examples are included to demonstrate the methodology concretely, properties of the estimator are discussed in detail, and a Monte Carlo simulation study is included to investigate the behaviour of a multi-parameter item response theory model using three competing finite-difference algorithms.

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Section: Advantages Of the Oakes' Identity Approximationmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Numerical approximation of the observed information matrix with Oakes' identity

Chalmers

2018

Brit J Math & Statis

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“…Default approaches for estimating standard errors also vary across programs, and it is important for the user to choose an approach that is computationally feasible, but also reasonably accurate. Although it is outside the scope of this paper to make a particular recommendation, standard error estimation is the topic of much recent research (Tian et al, 2013;Paek and Cai, 2014;Pritikin, 2017;Chalmers, 2018).…”

Section: Results Of Fitted Modelsmentioning

confidence: 99%

Estimation of Response Styles Using the Multidimensional Nominal Response Model: A Tutorial and Comparison With Sum Scores

Falk

2020

Front. Psychol.

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Recent years have seen a dramatic increase in item response models for measuring response styles on Likert-type items. These model-based approaches stand in contrast to traditional sum-score-based methods where researchers count the number of times that participants selected certain response options. The multidimensional nominal response model (MNRM) offers a flexible model-based approach that may be intuitive to those familiar with sum score approaches. This paper presents a tutorial on the model along with code for estimating it using three different software packages: flexMIRT ® , mirt, and Mplus. We focus on specification and interpretation of response functions. In addition, we provide analytical details on how sum score to scale score conversion can be done with the MNRM. In the context of a real data example, three different scoring approaches are then compared. This example illustrates how sum-score-based approaches can sometimes yield scores that are confounded with substantive content. We expect that the current paper will facilitate further investigations as to whether different substantive conclusions are reached under alternative approaches to measuring response styles.

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“…Unfortunately, these matrices are more complicated to compute for IRT models than for many other types of statistical models, particularly when the EM algorithm is adopted during estimation (Bock & Aitkin, 1981). Recently, however, Chalmers (2018a) demonstrated an accurate and efficient numerical scheme to obtain the observed information matrix which capitalize on Oakes' (1999) identity (see also Pritikin, 2017).…”

Section: Models and Estimationmentioning

confidence: 99%

Model Selection of Nested and Non-Nested Item Response Models Using Vuong Tests

Schneider

Chalmers

Debelak

et al. 2019

Multivariate Behavioral Research

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In this paper, we apply Vuong's (1989) general approach of model selection to the comparison of nested and non-nested unidimensional and multidimensional item response theory (IRT) models. Vuong's approach of model selection is useful because it allows for formal statistical tests of both nested and non-nested models. However, only the test of non-nested models has been applied in the context of IRT models to date.After summarizing the statistical theory underlying the tests, we investigate the performance of all three distinct Vuong tests in the context of IRT models using simulation studies and real data. In the non-nested case we observed that the tests can reliably distinguish between the graded response model and the generalized partial credit model. In the nested case, we observed that the tests typically perform as well as or sometimes better than the traditional likelihood ratio test. Based on these results, we argue that Vuong's approach provides a useful set of tools for researchers and practitioners to effectively compare competing nested and non-nested IRT models.

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A comparison of parameter covariance estimation methods for item response models in an expectation-maximization framework

Cited by 14 publications

References 21 publications

Numerical approximation of the observed information matrix with Oakes' identity

Numerical approximation of the observed information matrix with Oakes' identity

Estimation of Response Styles Using the Multidimensional Nominal Response Model: A Tutorial and Comparison With Sum Scores

Model Selection of Nested and Non-Nested Item Response Models Using Vuong Tests

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