Assessing the Fit of IRT Models in Language Testing. Muhammad Naveed Khalid Ardeshir Geranpayeh. Outline. Item Response Theory (IRT) Importance of Model Fit within IRT Fit Procedures Issues and Limitations Lagrange Multiplier (LM) Test An empirical study using LM Fit statistics
Muhammad Naveed Khalid
IRT applications in language testing are mainly used in
The utility of the IRT model is dependent upon the extent to which the model accurately reflects the data
Measurement Invariance (MI): Item responses can be described by the same parameters in all sub-populations.
Item Characteristic Curve (ICC): Describes the relation between the latent variable and the observable responses to items.
Local Independence (LI):Responses to different items are independent given the latent trait variable value.
Yen (2000) and Wainer & Thissen (2003) have shown the inadequacy of model-data fit
Some of the adverse consequences are:
Chi – Square Statistics
Tests of the discrepancy between the observed and expected frequencies.
Pearson-Type Item-Fit Indices (Yen, 1984; Bock, 1972).
Likelihood Ratio Based Item-Fit Indices (McKinley & Mills, 1985).
Glas(1999) proposed the LM test to the evaluation of model fit.
The LM tests are used for testing a restricted model against a more general alternative one.
Consider a null hypothesis about a model with parameters
This model is a special case of a general model with parameters
MI / DIF