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. |