An Introduction to Monte Carlo Simulations in Criminal Psychology
Applications in Evaluating Biased Estimators for Recidivism
Published in: Journal of Criminal Psychology, v. 5, no. 2, 2015, p.149-156
Posted on RAND.org on March 18, 2016
PURPOSE: Studies in criminal psychology are inevitably undertaken in a context of uncertainty. One class of methods addressing such uncertainties is Monte Carlo (MC) simulation. The purpose of this paper is to provide an introduction to MC simulation for representing uncertainty and focusses on likely uses in studies of criminology and psychology. In addition to describing the method and providing a step-by-step guide to implementing a MC simulation, this paper provides examples using the Fragile Families and Child Wellbeing Survey data. Results show MC simulations can be a useful technique to test biased estimators and to evaluate the effect of bias on power for statistical tests. DESIGN/METHODOLOGY/APPROACH: After describing MC simulation methods in detail, this paper provides a step-by-step guide to conducting a simulation. Then, a series of examples are provided. First, the authors present a brief example of how to generate data using MC simulation and the implications of alternative probability distribution assumptions. The second example uses actual data to evaluate the impact that omitted variable bias can have on least squares estimators. A third example evaluates the impact this form of heteroskedasticity can have on the power of statistical tests. FINDINGS: This study shows MC simulated variable means are very similar to the actual data, but the standard deviations are considerably less in MC simulation-generated data. Using actual data on criminal convictions and income of fathers, the authors demonstrate the impact of omitted variable bias on the standard errors of the least squares estimator. Lastly, the authors show the p-values are systematically larger and the rejection frequencies correspondingly smaller in heteroskedastic error models compared to a model with homoskedastic errors. ORIGINALITY/VALUE: The aim of this paper is to provide a better understanding of what MC simulation methods are and what can be achieved with them. A key value of this paper is that the authors focus on understanding the concepts of MC simulation for researchers of statistics and psychology in particular. Furthermore, the authors provide a step-by-step description of the MC simulation approach and provide examples using real survey data on criminal convictions and economic characteristics of fathers in large US cities.
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