Indexing Notation

Our notation is a generalization of King et al. designed to accommodate our enhancements to the various models. We index survey questions, response categories, and respondents as follows:

• We index survey questions by the pair $(s,j)$ , where question set $s$ ( $s=1,\dots,S$ ) corresponds to the self-assessment question number and refers to the set of questions that includes the self-assessment question (indicated by $j=0$ ) and, optionally, one or more vignette questions (indicated by $j=1,\dots,J_s$ ).

• We index response categories by $k$ ( $k=1,\dots,K_s$ ) separately for each survey question since they can each have different response categories. Each set of questions (self-assessment and vignettes) must have the same number of choice categories (coded as increasing sequential integers starting with 1). Missing values (whether structural, because the question was not asked, or due to nonresponse) should be coded as $k=0$ .

• We index respondents by $i$ or $\ell$ . Respondent $i$ ( $i=1,\dots,n$ ) is asked all of the self-assessment questions. Respondent $\ell$ ( $\ell=1,\dots,N$ ) is asked all of the vignette questions. (Respondents are indexed for self-assessment and vignette questions separately since each could be asked of independent samples; if they are asked of the same individuals, then $i=\ell$ and $n=N$ .) If your survey design asks each set of vignette questions in separate samples (and separate from the self-assessment question), then index each set of vignettes according to unique values of $\ell$ and use the missing value code ($k=0$ ) for vignettes that are not asked of a subgroup; in other words, stack the data in block diagonal format.

Thus, every mathematical symbol in the model could be indexed by $s$ , $j$ , $k$ , and either $i$ or $\ell$ . In practice, we drop indices that are constant.