Missing Data and the Rasch Model: The Effects of Missing Data Mechanisms on Item Parameter Estimation.

Area of Science:

• Psychometrics
• Statistical modeling
• Educational measurement

Background:

• Missing data is a common issue in psychometric research.
• The Rasch measurement model is widely used for item response theory analysis.
• Understanding the impact of missing data on Rasch model parameters is crucial for accurate measurement.

Purpose of the Study:

• To investigate the influence of missing data mechanisms (MCAR, MAR, MNAR), missing proportions, sample size, and test length on item parameter bias and standard errors within the Rasch model.
• To determine the conditions under which the Rasch model provides unbiased item parameter estimates despite missing data.

Main Methods:

• A simulation study was conducted to systematically vary missing data characteristics.
• The Rasch measurement model was applied to simulated datasets with different missing data scenarios.
• Bias and standard errors of item parameters were analyzed across conditions.

Main Results:

• Item parameters remained unbiased under missing completely at random (MCAR) and missing at random (MAR) conditions.
• Missing not at random (MNAR) data led to significant item parameter bias, particularly with higher missing proportions.
• Standard errors were primarily influenced by sample size, decreasing with larger samples.
• Standard errors were inflated under MCAR and MAR, but comparable to complete data under MNAR.

Conclusions:

• The Rasch model demonstrates robustness to missing data when the missingness mechanism is MCAR or MAR.
• MNAR data poses a substantial threat to the validity of Rasch model item parameter estimates.
• Researchers should carefully consider the missing data mechanism in their analyses; MNAR requires specific handling strategies.