Using item mean squares to evaluate fit to the Rasch model

Area of Science:

• Psychometrics
• Statistical modeling

Background:

• Rasch fit mean squares were extensively studied in the 1970s, leading to transformations into t-statistics.
• Sample size significantly influences Rasch fit mean squares, prompting the development of standardized critical values.
• A shift occurred in the late 1980s/early 1990s towards using untransformed fit mean squares due to sample size sensitivity in t-converted statistics.

Purpose of the Study:

• To trace the historical evolution of Rasch fit indices and their transformations.
• To investigate the effect of sample size on both untransformed fit mean squares and their t-transformed counterparts.
• To focus on item fit mean squares due to the limited impact of sample size on person fit mean squares.

Main Methods:

• Historical review of Rasch fit index development and transformations.
• Empirical examination of the influence of sample size on item fit mean squares.
• Analysis of the impact of sample size on t-transformed fit mean squares.

Main Results:

• The study details the historical trajectory of Rasch fit mean squares and their t-transformations.
• It highlights the differential impact of sample size on fit mean squares and their t-transformed values, particularly for item fit.
• Findings underscore the complexities introduced by sample size variations in Rasch model fit assessment.

Conclusions:

• Understanding the historical context and sample size effects is crucial for accurate Rasch model fit interpretation.
• The paper provides insights into the appropriate use of fit indices in Rasch analysis.
• Recommendations for best practices in applying fit mean squares and their transformations are implied.