Figure 1.

The x-axis variable is θ₁, the underlying construct measured by the first scale and the y-axis variable is θ₂, the underlying construct measured by the second scale; the illustration is for the PROMIS pediatric and adult Anxiety scales. Both scales report scores in T-score units. The IRT model distributions on θ₁ for two response patterns on the pediatric Anxiety scale are shown along the x-axis, along with the corresponding bivariate distributions, and those implied by calibrated projection on θ₂. The darker blue and red lines and curves on the θ₂ axis show the normal approximations to the projected posterior distributions computing using the linear approximation, based on the regression (solid black) line, and the combination of the variances of the θ₁ distributions and the variance around the regression line.