Linking Item Response Model Parameters

Linden, Willem J. van der; Barrett, Michelle D.

doi:10.1007/s11336-015-9469-6

Cited by 28 publications

(22 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, a CFA model (for continuous items) with two standardized factors and two items per factor is identified, but when the factor correlation is zero, the remaining parameters are not identified; an otherwise identified mixture model is not identified when a mixture component (that involves unique parameters) has zero probability; a model with a covariance matrix of random effects parametrized in Cholesky decomposition is not identified when the true value of this covariance matrix is singular; a fixed effect 3PL IRT model can be identified by fixing the slope and difficulty of one item (Wu, accepted), but that is not enough for a fixed effect Rasch model with guessing (van der Linden and Barrett, 2016). These singularities occur at a lower dimensional subset of the parameter space, so they do not affect the identification of the model for almost the whole parameter space.…”

Section: Singularitiesmentioning

confidence: 99%

Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes

2016

View full text Add to dashboard Cite

This article considers the identification conditions of confirmatory factor analysis (CFA) models for ordered categorical outcomes with invariance of different types of parameters across groups. The current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model. This approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways. Once an invariance condition is imposed on a parameter, these identification conditions may become restrictions and define statistically non-equivalent models, leading to different conclusions. By analyzing the transformation that leaves the model-implied probabilities of response patterns unchanged, we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model. Tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model.

show abstract

Section: Singularitiesmentioning

confidence: 99%

Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes

2016

View full text Add to dashboard Cite

show abstract

“…Item parameters are often treated as if they are known and without error when used in many IRT applications, such as latent trait estimation (see Baker & Kim, 2004;Cheng & Yuan, 2010), scale linking and equating (van der Linden & Barrett, 2016), and computerized adaptive testing (Patton, Cheng, Yuan, & Diao, 2013). If they are not estimated accurately, using item parameter estimates in those applications can cause many undesirable consequences (Cheng, Liu, & Behrens, 2015;Patz & Junker, 1999;Tsutakawa & Johnson, 1990).…”

Section: Robust Estimation Of Grm Through Robust Maximum Marginal Likmentioning

confidence: 99%

Robust maximum marginal likelihood (RMML) estimation for item response theory models

Hong

Cheng

2018

Behav Res

View full text Add to dashboard Cite

Self-report data are common in psychological and survey research. Unfortunately, many of these samples are plagued with careless responses, due to unmotivated participants. The purpose of this study was to propose and evaluate a robust estimation method to detect careless or unmotivated responders, while leveraging item response theory (IRT) person-fit statistics. First, we outlined a general framework for robust estimation specific for IRT models. Subsequently, we conducted a simulation study covering multiple conditions in order to evaluate the performance of the proposed method. Ultimately, we showed that robust maximum marginal likelihood (RMML) estimation significantly improves detection rates for careless responders and reduces bias in item parameters across conditions. Furthermore, we applied our method to a real data set, to illustrate the utility of the proposed method. Our findings suggest that robust estimation coupled with person-fit statistics offers a powerful procedure to identify careless respondents for further review and to provide more accurate item parameter estimates in the presence of careless responses.

show abstract

“…Linking requires selection of a linking design and inference of the function that maps the true values of the parameters in one calibration onto the values that would have been obtained for the identifiability restrictions used in the other calibration. van der Linden and Barrett (2016) proved linking functions for monotone response models are always component-wise monotone and consequently for the 3PL model they can be contained as the solution to the functional equation…”

Section: Linking Functions Designs and Equationsmentioning

confidence: 99%

“…First, we will review the linking functions for the 3PL model recently derived directly from the presence of different identifiability restrictions in different calibrations (van der Linden & Barrett, 2016). The derivation did prove the generally assumed linearity of the linking functions currently in use for the θ p , a i , and b i parameters but provided definitions of their parameters that deviated from those used in the current methods.…”

mentioning

confidence: 99%

Estimating Linking Functions for Response Model Parameters

Barrett¹,

Linden

2018

Journal of Educational and Behavioral Statistics

Self Cite

View full text Add to dashboard Cite

Parameter linking in item response theory is generally necessary to adjust for differences between the true values for the same item and ability parameters due to the use of different identifiability restrictions in different calibrations. The research reported in this article explores a precision-weighted (PW) approach to the problem of estimating the linking functions for the common dichotomous logistic response models. Asymptotic standard errors (ASEs) of linking for the new approach are derived and compared to those of the mean/mean and mean/sigma linking methods to which it has a superficial similarity and to the Haebara and Stocking and Lord response function methods. Empirical examples from a few recent linking studies are presented. It is demonstrated that the new approach has smaller ASE than the mean/mean and mean/sigma methods and comparable ASE to the response function methods. However, when some of the item parameters have large estimation error relative to the others, all current methods appear to violate the rather obvious requirement of monotone decrease in ASE with the number of common items in the linking design while the ASE of the PW method demonstrates monotone decrease with the number of common items. The PW method also has the benefits of simple calculation and an ASE which is additive in the contribution of each item, useful for optimal linking design. We conclude that the proposed approach to estimating linking parameters holds promise and warrants further research.

show abstract

Linking Item Response Model Parameters

Cited by 28 publications

References 45 publications

Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes

Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes

Robust maximum marginal likelihood (RMML) estimation for item response theory models

Estimating Linking Functions for Response Model Parameters

Contact Info

Product

Resources

About