The two-parameter logistic model (Birnbaum, 1968; Lord and Novick, 1968), an extension of the Rasch or one-parameter logistic model (Rasch, 1960), was used to define the relationship between the observed responses to the criteria and the underlying unobserved latent trait or construct (cannabis use disorder severity). This Item Response Theory (IRT) model was generated using the marginal maximum likelihood estimates (Bock and Aitken, 1981; Harwell et al., 1988) of two parameters: the b or threshold parameter, and the a or discrimination parameter. The BILOG-MG statistical program was used for this purpose (Scientific Software International, 2003). The a parameter measures the ability of a criterion to discriminate people who are higher on the continuum from those who are lower on the continuum. This parameter describes how strongly the criterion is related to the underlying trait or construct. The larger the a parameter (i.e., the slope at its steepest point), the greater the discrimination of a criterion. The b or threshold parameter measures the severity of a criterion; criteria with high thresholds are endorsed less frequently and are therefore considered “more severe”.
