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NAEP Analysis and Scaling → Estimation of NAEP Score Scales → Item Scaling Models → The Three-Parameter Logistic Model
NAEP Technical DocumentationThe Three-Parameter Logistic Model
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A three-parameter logistic (3PL) model is used for the multiple-choice items (which are scored correct or incorrect.) The fundamental equation of the 3PL model defines the probability that a person whose score on scale k is characterized by the unobservable variable θk will respond correctly to item j as
where
| xj | is the response score for item j, 1 if correct and 0 if not; |
|
| aj | where aj > 0, is the slope parameter of item j, characterizing its sensitivity to scale score; |
|
| bj | is the threshold parameter of item j, characterizing its difficulty; and | |
| cj | where 0 < cj < 1, is the lower asymptote parameter of item j, reflecting the chances of students of very low scale score selecting the correct option. |
The probability of an incorrect response to the item is further defined as
Last updated 14 July 2008 (DB)
