A constrained factor mixture analysis model for consistent and inconsistent respondents to mixed-worded scales
Mixed-worded scales require a more careful reading and answering process than scales with only one type of wording. The present study is about the unintended consequences of using such scales, because typically, not all respondents answer positively and negatively worded items consistently. This population heterogeneity—meaning that there are distinct groups of consistently and inconsistently answering respondents—may arguably underlie wording-related effects in mixed-worded scales. We formulated a constrained factor mixture analysis model that operationalized these two assumed classes of respondents. We investigated five data sets that contained four mixed-worded attitude scales, large-scale samples from three countries (Germany, Australia, and the U.S.), and two age groups (children and adolescents). The constrained factor mixture analysis model showed estimated parameter patterns in line with theoretical expectations and consistently outperformed its more traditional competitor, confirmatory factor analysis with one global and one orthogonal method factor across all used data sets. We found proportions of between 7% and 20% of respondents belonging to the inconsistent classes. To further substantiate and validate the interpretation of the proposed model, we related class membership to theoretically relevant respondent characteristics such as reading achievement, cognitive skills, or conscientiousness. Further, we undertook an initial exploration of the overlap in inconsistent respondents’ class membership across time and across scales within a survey.