Our IRT analysis began by hypothesizing a continuous latent variable representing the alcohol use disorder continuum, referred to as θ, which is normally distributed with mean 0 and standard deviation 1. The 2-parameter logistic IRT provides estimates of the discrimination (parameter a) and severity (parameter b) of each item indexing this continuum. Discrimination is defined as the ability of the criterion to distinguish between those who are higher on the alcohol use disorder continuum versus those who are lower. Severity is defined as the point along the continuum when there is a 50% chance of the item being present. Note that severity is directly related to the prevalence of the criterion in the data; in most cases criteria that are rare are more clinically severe, but higher severity in the IRT model does not necessarily indicate higher clinical severity. The formula for calculating the probability of item endorsement in MPLUS (Muthén & Asparouhov, 2002) is: P(u=1∣θ)=1/1+e−Da(θ−b)
