Model Information

Variance Components

Rating Scale Thresholds

Fit Diagnostic Diagrams

Scatter plots showing Measure vs. Fit statistic for each facet. Points outside the threshold lines may indicate misfit. Red = misfit, Blue = acceptable fit.

Wright Map displays all facets on a common logit scale.

Higher = Higher ability / More severe / More difficult

Variance Explained by Rasch Measures

This table shows how much of the variance in the observed scores is explained by the Rasch model measures (person ability, rater severity, task difficulty, etc.).

Category Probability Curves

This plot shows how the probability of each rating category changes across the logit scale. Each number represents the category most likely to be selected at that point on the scale.

Rating Scale Threshold Analysis

This analysis evaluates the rating scale structure based on Linacre (2002) guidelines, including threshold ordering, category frequencies, and step advances.

Bias/Interaction Analysis

This analysis detects systematic patterns in how specific raters rate specific tasks or persons differently than expected. Significant biases (|t| >= 2.0) indicate interactions that may affect measurement fairness.

Bias/Interaction Pairwise Report

Pairwise comparisons of bias measures for each target element across context elements. Contrasts with |t| >= 2.0 indicate significant differences in how a target element interacts with two context elements.

Unexpected Responses (Table 4)

This table lists observations with standardized residuals |StRes| >= 3.0, indicating ratings that are unexpectedly high or low given the model estimates. These responses may warrant investigation for data entry errors or unusual patterns.

PCA of Standardized Residuals

Principal Component Analysis of standardized residuals to assess unidimensionality. If the 1st contrast eigenvalue exceeds 2.0, a secondary dimension may be present in the data, which could threaten the Rasch model's unidimensionality assumption.

Item Loadings on Residual Contrasts

Biplot (1st and 2nd Contrasts)

Export Report

Select the sections to include in the report and choose an output format.

Many-Facet Rasch Measurement (MFRM) extends the Rasch model to analyze multiple facets simultaneously (persons, raters, tasks, criteria).

• Person ability: Higher = more proficient
• Rater severity: Higher = stricter rater
• Task difficulty: Higher = harder task
• Criterion difficulty: Higher = harder criterion (4-facet)

You can specify custom column names in the Data Input tab. The app will map your column names to the internal facet roles (Person, Rater, Task, Criterion, Score). Default names: Person, Rater, Task, Criterion, Score.

This app uses Joint Maximum Likelihood Estimation (JMLE). The default score model is the Rating Scale Model (RSM) with common thresholds across all observations. You can optionally switch to the Partial Credit Model (PCM) with facet-specific thresholds. PCM can be applied to any facet (person, rater, task, or criterion), allowing each element of the selected facet to have its own rating scale structure (cf. WIDA TR-2024-1, Linacre/FACETS).

• Infit MNSQ: Variance-weighted mean square residual (expected = 1.0)
• Outfit MNSQ: Unweighted mean square residual (expected = 1.0)
• Acceptable range: 0.5 - 1.5 (or 0.7 - 1.3 for high-stakes)

Linacre, J. M. (1994). Many-Facet Rasch Measurement. MESA Press.

Linacre, J. M. (2002). Optimizing rating scale category effectiveness. Journal of Applied Measurement, 3(1), 85-106.

Linacre, J. M. (2024). FACETS Rasch measurement computer program. Winsteps.com.

Atsushi MIZUMOTO, Ph.D.
Taichi YAMASHITA, Ph.D.
Kansai University, Osaka, Japan