Selecting a Dichotomous IRT ModelNumerous IRT models are available for examining dichotomous data. Ultimately the choice of a model should be based on both theoretical and empirical considerations, i.e., model-data fit.One of the most commonly used models among applied psychologists is the Three-Parameter Logistic Model (3PL). 3PL has been used primarily for modeling cognitive ability data, but recently 3PL has been applied to personality data as well (See Embretson and Reise [2000] for a description of other applications). Description of The Three Parameter Logistic Model (3PL)The 3PL model is a more general form of the one parameter (1PL or Rasch Model) and two parameter logistic model (2PL; Birnbaum, 1968). It contains three parameters representing item discrimination(a), item location(b), as well as a lower asymptote parameter(c). Note that the 2PL model can be obtained from 3PL be setting c=0; the 1PL model may be obtained by setting c=0 and a=1. The mathematical form of the 3PL model is shown below. where:
A representative 3PL item response function (IRF) is shown below:  The "a" parameter affects the steepness of the curve; as "a" increases the slope of the IRF increases. Larger "a" parameters provide better discrimination among examinees. To see how the "a" parameter influences the slope of an IRF, click below. 
"a" Parameter Previous Next The "b" parameter represents the location of the IRF along the horizontal axis, theta. It is commonly called the item difficulty, or threshold, parameter. "b" is related to the proportion-correct score, "p," in classical test theory, but the two are inversely related. Large values of "p" indicate relatively "easy" items, whereas large values of "b" indicate "difficult" items. Note that, when c=0, "b" equals the value of theta which the probability of a positive response is 0.5. To see how the "b" parameter influences the location of an IRF, click below. 
"b" Parameter Previous Next The "c" parameter is commonly called the "pseudo-guessing" parameter, because it indicates the probability of responding positively for examinees having very low theta. To see how the "c" parameter influences the shape of an IRF, click below. 
"c" Parameter Previous Next |