Estimating SEM with Ordinal Data and Scale Usage Heterogeneity

In the social sciences, it is often useful to introduce latent variables and usestructural equation modeling to quantify relations among observable and latentvariables. Data gathered through surveys is frequently ordinal in nature, asLikert-scale type questions are used in most questionnaires. Although a large numberof publications shows that treating ordinal data as metric can lead to wrong results,this practice is still common. Moreover, respondents treat the rating scales differently.There may be ”yeah”-sayers whose responses are biased in the positive direction (orthe opposite). Some respondents may also use some part of the scale only. Thisproblem can be explicitly addressed by modeling heterogeneity scale usage. This noteshows how to estimate SEM with ordinal data and scale usage heterogeneity.