Modelling general patterns of digit preference

Abstract

In many applications data can be interpreted as indirect observations of a latent distribution. A typical example is the phenomenon known as digit preference, i.e. the tendency to round outcomes to pleasing digits. The composite link model (CLM) is a useful framework to uncover such latent distributions. Moreover, when applied to data showing digit preferences, this approach allows estimation of the proportions of counts that were transferred to neighbouring digits. As the estimating equations generally are singular or severely ill-conditioned, we impose smoothness assumptions on the latent distribution and penalize the likelihood function. To estimate the misreported proportions, we use a weighted least-squares regression with an added L1 penalty. The optimal smoothing parameters are found by minimizing the Akaike’s information Criterion (AIC). The approach is verified by a simulation study and several applications are presented.