Random parameter structure and the testlet model: extension of the Rasch testlet model.

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• The Rasch testlet model (RT) assumes independence between testlet effects and the target dimension.
• Violations of this assumption can impact model performance and parameter estimation accuracy.

Purpose of the Study:

• To investigate the impact of violating the independence assumption in the Rasch testlet model (RT).
• To evaluate the performance of an extended Rasch testlet model (ET) that estimates the variance-covariance matrix without constraints.

Main Methods:

• Computer simulations were employed to compare the performance of RT and ET.
• The study focused on scenarios with correlated testlet effects and target dimensions.

Main Results:

• The extended Rasch testlet model (ET) demonstrated equal or superior performance compared to the standard Rasch testlet model (RT).
• The target dimension variance was the most affected parameter in RT, with bias increasing under high testlet effect and correlation.
• RT showed comparable performance to ET in estimating item and testlet effect parameters.

Conclusions:

• The extended Rasch testlet model (ET) provides a more robust approach when the independence assumption is violated.
• Accurate assessment of testlet effects relative to target dimensions can be challenging with the standard Rasch testlet model (RT) in certain real-world applications.