Supervised Classes, Unsupervised Mixing Proportions: Detection of Bots in a Likert-Type Questionnaire

Administering Likert-type questionnaires to online samples risks contamination of the data by malicious computer-generated random responses, also known as bots. Although nonresponsivity indices (NRIs) such as person-total correlations or Mahalanobis distance have shown great promise to detect bots, universal cutoff values are elusive. An initial calibration sample constructed via stratified sampling of bots and humans-real or simulated under a measurement model-has been used to empirically choose cutoffs with a high nominal specificity. However, a high-specificity cutoff is less accurate when the target sample has a high contamination rate. In the present article, we propose the supervised classes, unsupervised mixing proportions (SCUMP) algorithm that chooses a cutoff to maximize accuracy. SCUMP uses a Gaussian mixture model to estimate, unsupervised, the contamination rate in the sample of interest. A simulation study found that, in the absence of model misspecification on the bots, our cutoffs maintained accuracy across varying contamination rates.