Table 1.

Common terms used in an IRT graded response model

Term	Abbreviation/Symbol	Description
Slope parameter	a	• 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	bij	• 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.
Theta	Θ	• Latent variable being measured (e.g., depression).
Item characteristic curve	ICC	• 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	TCC	• Sum of the ICCs across all items. • Shows the expected total summed score on the scale for each level of theta.
Item information function	IIF	• 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	TIF	• Sum of the item information functions across all items. • Indicates where along theta the scale has the greatest measurement precision.
Item fit	S-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 dependence	LD	• 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	DIF	• Measurement bias in an item between two or more groups while holding the latent trait level constant.