Fig. 1
From: Who are those random responders on your survey? The case of the TIMSS 2015 student questionnaire
Note Symbols follow standard path diagram conventions, with squares representing observed variables (i.e., item responses); circles, latent variables (i.e., trait to be measured by the scale of items); arrows indicating dependence relations; vertical lines, response category thresholds. Typical responders a conditional independence given the latent trait; Random responders b mutual independence with uniformly distributed response categories (cf. squares divided into equal parts and no relation with circle or other squares). Reprinted under the terms of CC-BY-NC from van Laar and Braeken (2022), Journal of Educational Measurement
Mixture IRT model Framework to Define and Operationalize Random Responders in terms of Independence and Uniformity of Item Responses.