|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.|