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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




Slope parameter


• 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 parameters


• 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.



• Latent variable being measured (e.g., depression).

Item characteristic curve


• 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 curve


• Sum of the ICCs across all items.

• Shows the expected total summed score on the scale for each level of theta.

Item information function


• 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 function


• Sum of the item information functions across all items.

• Indicates where along theta the scale has the greatest measurement precision.

Item fit


• 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 dependence


• 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 functioning


• Measurement bias in an item between two or more groups while holding the latent trait level constant.