Abstract
For reasons of methodological convenience statistical models analysing judicial decisions tend to focus on the duration of custodial sentences. These types of sentences are however quite rare (7% of the total in England and Wales), which generates a serious problem of selection bias. Typical adjustments employed in the literature, such as Tobit models, are based on questionable assumptions and are incapable to discriminate between different types of non-custodial sentences (such as discharges, fines, community orders, or suspended sentences). Here we implement an original approach to model custodial and non-custodial sentence outcomes simultaneously avoiding problems of selection bias while making the most of the information recorded for each of them. This is achieved by employing Pina-Sánchez et al. (Br J Criminol 59:979–1001, 2019) scale of sentence severity as the outcome variable of a Bayesian regression model. A sample of 7242 theft offences sentenced in the Crown Court is used to further illustrate: (a) the pervasiveness of selection bias in studies restricted to custodial sentences, which leads us to question the external validity of previous studies in the literature limited to custodial sentence length; and (b) the inadequacy of Tobit models and similar methods used in the literature to adjust for such bias.