The development of delinquency during adolescence: a comparison of missing data techniques revisited

Conclusions about the individual development of delinquent behaviours during the life-course are often made by repeatedly interviewing the same respondents (i.e. panel data). Missing data, especially unit nonresponse and panel attrition are often a problem for the analysis of panel data, as they pose a threat to the validity of statistical inferences. Multiple imputation (MI) is a standard state-of-the-art technique to address these problems. However, until very recently, MI methods to impute highly skewed, zero-inflated and repeatedly measured count data such as the count of delinquent behaviours per year, were not available. Solutions that were often applied included data transformations and rounding, so that available MI methods, usually based on the multivariate normal model, could be applied. This approach has also been used by Reinecke and Weins (Qual Quant 47(6):3319–3334, 2013), who analysed delinquency data from an adolescents’ four-wave panel. Recent missing data research, however, suggests that these “normalizing” practices could be problematic and that imputation models with implausible distributional assumptions should generally be avoided when the empirical data depart too heavily from these assumptions. In the present paper, we re-analyse the data from Reinecke and Weins (2013) using MI models, where parametric assumptions of the imputation model are compatible to the subsequent analysis model (a growth curve model for zero-inflated count data). Results show that the chance of reporting zero punishable offences decreases over time, with a turning point at around the age of 15. Likewise, the versatility of delinquent behaviours increases early on in adolescence, and decreases later (reflecting the typical age-crime curve). Boys and students from the bottom-level branch of the German educational system exhibit a higher versatility in delinquent activity. A comparison of present results with the original ones from Reinecke and Weins (2013) corroborates recommendations e.g. by Yu et al. (Stat Methods Med Res 16(3):243–258, 2007) to opt for missing data methods with fitting distributional assumptions.