Linking Error in the 2PL Model

Abstract

The two-parameter logistic (2PL) item response model is likely the most frequently applied item response model for analyzing dichotomous data. Linking errors quantify the variability in means or standard deviations due to the choice of items. Previous research presented analytical work for linking errors in the one-parameter logistic model. In this article, we present linking errors for the 2PL model using the general theory of M-estimation. Linking errors are derived in the case of log-mean-mean linking for linking two groups. The performance of the newly proposed formulas is evaluated in a simulation study. Furthermore, the linking error estimation in the 2PL model is also treated in more complex settings, such as chain linking, trend estimation, fixed item parameter calibration, and concurrent calibration.

Gender-Based Differential Item Function for the Positive and Negative Semantic Dimensions of the Relationship Satisfaction Scale with Item Response Theory

“…The first is that the MIMIC model adopted here only examines uniform DIF [74], which means that non-uniform DIF may have existed but may not have been detected. In future research, scholars can adopt other methods of assessing DIF that are able to detect non-uniform DIF, such as logistic regression and the IRT model [74,[82][83][84][85] and quantify the impact of DIF on mean comparisons by a variance measure by linking errors, either by analytical treatments [86] or with resampling techniques [87]. Second, the probability of Type I errors in this study was inflated because we did not test the clinical meaning of DIF using qualitative methods, which is considered a best practice [88].…”

Estimation of Standard Error, Linking Error, and Total Error for Robust and Nonrobust Linking Methods in the Two-Parameter Logistic Model

“…The total error (TE) includes both sources of uncertainty: the standard error due to randomness due to persons and the linking error due to randomness in items [47,50,51,64]. However, it has been argued that the ordinary linking error estimate is partly affected by the sampling error [65]. In this article, a bias-corrected linking error resulting in a bias-corrected total error estimate is examined to try to reduce the portion of the estimated linking error variance that is due to the sampling error.…”

“…In this section, we derive the standard error, linking error, and total error for linking estimates in the framework of M-estimation theory [58,59,76]. The treatment in this section is an extension of the material presented in [65]. Assume the item parameter estimate γ i = ( a i1 , b i1 , a i2 , b i2 ) with an estimated variance matrix V γ i .…”

“…We now compute the total uncertainty in δ (i.e., the total error). The variance as the total error has been defined as the sum of the variances due to the sampling error and linking error, and it is written as follows (see [50,65]):…”

To Check or Not to Check? A Comment on the Contemporary Psychometrics (ConPsy) Checklist for the Analysis of Questionnaire Items

“…I would like to see the approach of [64] being widely implemented in SEM/CFA software. In this approach, the extent of model error is reflected in increased standard errors [24,[64][65][66][67]. This would be a more honest strategy to acknowledge the extent of SEM/CFA model misspecification.…”