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Table 1 Common terms used in an IRT graded response model

From: State of the psychometric methods: patient-reported outcome measure development and refinement using item response theory

TermAbbreviation/SymbolDescription
Slope parametera• Also referred to as the discrimination parameter.
• Measures the strength of the relationship between the item and the latent variable being measured.
• Items with larger slopes are better able to distinguish between individuals with higher and lower levels of the latent variable being measured.
Threshold parametersbij• Also known as the location parameters or the difficulty/severity parameters.
• Represents the points along theta at which the corresponding response categories are the most discriminating or informative.
• Items with higher thresholds represent greater severity of the latent variable being measured.
ThetaΘ• Latent variable being measured (e.g., depression).
Item characteristic curveICC• Also referred to as a “trace line.”
• Visual image showing the probability of an item response across the range of theta (latent trait).
• Can reveal weak items and overlapping response categories.
Test characteristic curveTCC• Sum of the ICCs across all items.
• Shows the expected total summed score on the scale for each level of theta.
Item information functionIIF• Index of the precision in measurement in distinguishing between individuals with different levels of the latent variable being measured.
• More information indicates greater precision and reliability.
• Item information is peaked when the slope parameter is high.
• Standard error of measurement is inversely related to information.
Test information functionTIF• Sum of the item information functions across all items.
• Indicates where along theta the scale has the greatest measurement precision.
Item fitS-X2• Diagnostic statistic that examines goodness of fit of the IRT model for each item.
• Examines observed and expected response proportions for each item value.
• Significant result indicates item misfit.
Local dependenceLD• Statistic that examines bivariate fit to identify evidence of items that are excessively related given the common underlying construct.
• Significant result indicates content redundancy between two or more items.
Differential item functioningDIF• Measurement bias in an item between two or more groups while holding the latent trait level constant.
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