Numerical approximation of the observed information matrix with Oakes' identity

Chalmers, R. Philip

doi:10.1111/bmsp.12127

Cited by 28 publications

(42 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.

View full text Add to dashboard Cite

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.

show abstract

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.

View full text Add to dashboard Cite

show abstract

“…Guo, Ma, and de la Torre (2017) found that with misspecified Q-matrix, the standard error of item parameters estimated using the OPG approximation can be problematic, so future research may examine their influence on the performance of the Wald test. In addition, apart from the OPG, Louis’s, and sandwich information matrices investigated in this study, future research may explore the performance of the Wald test using covariance matrix calculated in other ways, such as the Oakes’s method (Chalmers, 2018) and the numerical differential methods (Jamshidian & Jennrich, 2000).…”

Section: Discussionmentioning

confidence: 99%

Category-Level Model Selection for the Sequential G-DINA Model

Torre

2018

Journal of Educational and Behavioral Statistics

View full text Add to dashboard Cite

Solving a constructed-response item usually requires successfully performing a sequence of tasks. Each task could involve different attributes, and those required attributes may be “condensed” in various ways to produce the responses. The sequential generalized deterministic input noisy “and” gate model is a general cognitive diagnosis model (CDM) for graded response items of this type. Although a host of dichotomous CDMs with different condensation rules can be used to parameterize the success probability of each task, specifying the most appropriate one remains challenging. If the CDM specified for each task is not in accordance with the underlying cognitive processes, the validity of the inference could be questionable. This study aims to evaluate whether several hypothesis tests, namely, the Wald test using various variance–covariance matrices, the likelihood ratio (LR) test, and the LR test using approximated parameters, can be used to select the appropriate CDMs for each task of graded response items. Simulation studies are conducted to examine the Type I error and power of the hypothesis tests under varied conditions. A data set from the Trends in International Mathematics and Science Study 2007 mathematics assessment is analyzed as an illustration.

show abstract

“…Throughout this paper, we utilized the observed information matrix results obtained via the Oakes identity approximation method described by Chalmers (2018a).…”

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Numerical approximation of the observed information matrix with Oakes' identity

Cited by 28 publications

References 56 publications

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

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

Category-Level Model Selection for the Sequential G-DINA Model

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

Contact Info

Product

Resources

About