The impact of measurement error in models using police recorded crime rates

Objectives: Assess the extent to which measurement error in police recorded crime rates impact the estimates of regression models exploring the causes and consequences of crime. Methods: We focus on linear models where crime rates are included either as the response or as an explanatory variable, in their original scale, or log-transformed. Two measurement error mechanisms are considered, systematic errors in the form of under-recorded crime, and random errors in the form of recording inconsistencies across areas. The extent to which such measurement error mechanisms impact model parameters is demonstrated algebraically, using formal notation, and graphically, using simulations. Results: Most coefficients and measures of uncertainty from models where crime rates are included in their original scale are severely biased. However, in many cases, this problem could be minimised, or altogether eliminated by log-transforming crime rates. This transforms the multiplicative measurement error observed in police recorded crime rates into a less harmful additive mechanism. Conclusions: The validity of findings from regression models where police recorded crime rates are used in their original scale is put into question. In interpreting the large evidence base exploring the effects and consequences of crime using police statistics we urge researchers to consider the biasing effects shown here. Equally, we urge researchers to log-transform crime rates before they are introduced in statistical models.