  Opinion dynamics models have an enormous potential for studying current
phenomena such as vaccine hesitancy. Unfortunately, to date, most of the models
have little to no empirical validation. One major problem in testing these
models against real-world data relates to the difficulties in measuring
opinions in ways that map directly to representations in models. Indeed, this
kind of measurement is complex in nature and presents more types of measurement
error than just classical random noise. Thus, it is crucial to know how these
different error types may affect the model's predictions. In this work, we
analyze this relationship in the Deffuant model. Starting from the
psychometrics literature, we first discuss how opinion measurements are
affected by three types of errors: random noise, binning, and distortions (i.e.
uneven intervals between scale points). While the first two are known to most
of the scientific community, the third one is mostly unknown outside
psychometrics. Because of that, we highlight the nature and peculiarities of
each of these measurement errors. By simulating these types of error, we show
that the Deffuant model is robust to binning but not to noise and distortions.
Indeed, if a scale has 4 or more points (like most self-report scales), binning
has almost no effect on the final predictions. However, prediction error
increases almost linearly with random noise, up to a maximum error of 40%.
After reaching this value, increasing the amount of noise does not worsen the
prediction. Distortions are most problematic, reaching a maximum prediction
error of 80%. Up to now most of the research focused on the properties of the
models without analyzing the types of data they may be used with. Here we show
that when studying a model, we should also analyze its robustness to these
types of measurement error.
