The Impact of Measurement Error in Regression 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

The impact of measurement error is highly variable across different settings. Depending on the crime type, the spatial resolution, but also where and how police recorded crime rates are introduced in the model, the measurement error induced biases could range from negligible to severe, affecting even estimates from explanatory variables free of measurement error. We also demonstrate how in models where crime rates are introduced as the response variable, the impact of measurement error could be eliminated using log-transformations.

Conclusions

The validity of a large share of the evidence base exploring the effects and consequences of crime is put into question. In interpreting findings from the literature relying on regression models and police recorded crime rates, we urge researchers to consider the biasing effects shown here. Future studies should also anticipate the impact in their findings and employ sensitivity analysis if the expected measurement error induced bias is non-negligible.