1. For example, to estimate the AMCEs for the candidates' age levels we run the following regression rating ijk = θ 0 + θ 1[age ijk = 75] + θ 2[age ijk = 68] + θ 3[age ijk = 60] + θ 4[age ijk = 52] + θ 5[ageijk= 45] + ε ijk where rating ijk is the outcome variable that contains the rating and [age ijk = 68], [age ijk = 75], etc., are dummy variables coded 1 if the age of the candidate is 68, 75, etc., and 0 otherwise. The reference category is a 36-year-old candidate. Accordingly, , etc., are the estimators for the AMCEs for ages 68, 75, etc., compared to the age of 36. Note that, alternatively, we can obtain the equivalent estimates of the AMCEs along with the AMCEs of the other attributes by running a single regression of rating ijk on the combined sets of dummies for all candidate attributes, as explained in Section 4.1.
2. Estimating causal effects of treatments in randomized and nonrandomized studies.
3. Strictly speaking, the AMCE for the choice outcome only depends on the joint distribution of Tijk [–l] and Ti [–j]k after marginalizing p(t) with respect to Tijk. We opt for the simpler notation given in the main text.
4. The Use of Vignettes in Survey Research