Item response analysis. An item response analysis was conducted in Mplus 5.2 (Muthen and Muthen, 1998-2007), using only one member of each twin pair. Each AA and AD symptom was included as a categorical variable. Two parameters, difficulty (also called “threshold” [Langenbucher et al., 2004]) and discrimination, were estimated using a 2 parameter IRT model using a probit metric. As discussed by Takane and de Leeuw (1987), there is a direct equivalence of the normal ogive item response model to the factor analysis model for binary data. Essentially, the item difficulty parameters correspond to the item thresholds, while the discrimination parameters correspond to the factor loadings. Difficulty refers to the location on the underlying latent continuous liability to alcohol problems at which the probability of endorsing each symptom is 50%. Discrimination measures the degree to which a given symptom distinguishes individuals with liability levels below and above that symptom's difficulty location. A symptom with a low discrimination parameter does not effectively distinguish such individuals.
