Linking response quality to survey engagement: a combined random scale and latent variable approach

Recent interest in the topic of random scale heterogeneity in discrete choice data has led to the development of specialised tools such as the G-MNL model, as well as repeated claims that studies which fail to separate scale heterogeneity from heterogeneity in individual coefficients are likely to produce biased results. Contrary to this, Hess and Rose (2012) show that separate identification of the two components is not in fact possible in a random coefficients model using a typical linear in parameters specification, and that any gains in performance are potentially just the result of more flexible distributional assumptions. On the other hand, linking scale heterogeneity to measured characteristics of the respondents is likely to yield only limited insights, while using respondent reported measures of survey understanding or analyst captured measures such as survey response time puts an analyst at risk of measurement error and endogeneity bias. The contribution made in this paper is to put forward a hybrid model in which survey engagement is treated as a latent variable which is used to model the values of a number of indicators of survey engagement in a measurement model component, as well as explaining scale heterogeneity within the choice model. This model overcomes some of the shortcomings of earlier work, permitting us to link part of the heterogeneity across respondents to differences in scale, while also allowing us to make use of indicators of survey engagement without risk of endogeneity bias. Results from an empirical application show a strong link between the two model components as well as arguably more reasonable substantive outputs for the choice model component.