more probable than its absence. In the case of multiple symptoms, we have 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ p(Y_{{ij}} = 1) = \Phi (\theta _{j} - \beta _{i} ), $$\end{document}with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \Phi (.) $$\end{document} denoting the cumulative standard normal distribution function. That is, the probability of the presence of symptom i in person j is a function of both a person’s liability score θj and a symptom (or item) parameter βi. In the IRT framework, this model is referred to as the one-parameter normal ogive model, or 1PNO (Lawley 1943; Lord 1952, 1953). This model is identified with a location restriction, for example, μ = 0. The variance of the latent trait, σ2, can be estimated and can be interpreted as the covariance of the items: the larger the variance, the higher the reliability of the scale.
