Definition

Define $C_{is}$ as the self-assessment relative to the corresponding set of vignettes. For respondents with identical ordinal rankings for the vignettes ( $z_{i,j-1}<z_{ij}$ , $\forall\thinspace i,j$ ), let

$$C_{is} = \begin{cases}1 & \mbox{if $y_{is}<z_{i1}$}\\ 2 & \mbox{i... ...}$}\\ \vdots & \vdots \\ 2{J_s}+1 & \mbox{if $y_{is}>z_{i{J_s}}$}\\ \end{cases}$$ (1)

Respondents with ties in the vignette answers would reduce our knowledge of $C_{is}$ to a set of values rather than just one value. Inconsistencies in the ordinal ranking are grouped and treated as ties. When few categories exist with which to distinguish these categories, additional collapsing may occur.