Modelling Crime Rate Using a Mixed Effects Regression Model
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 6, November 2015, Pages: 496-503
Received: Oct. 2, 2015; Accepted: Oct. 15, 2015; Published: Oct. 28, 2015
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Chris Muchwanju, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
Joel Cheruyiot Chelule, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
Joseph Mung’atu, Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi, Kenya
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In this paper we propose a type of Mixed effects Regression Model, that is Hierarchical Linear Model to study crime rate. We derive the estimators of the proposed model and discuss the asymptotic properties of the model. In order to test for the practicability of the proposed model, we estimate a crime equation using a panel dataset of the provinces in Kenya for the period 1992 to 2012 employing the REML estimator. Our empirical results suggest that Poverty Rate, Unemployment rate, Probability of arrest, population Density and police rate are correlated to all typologies of crime rate considered. The results further suggest that crime rate is better explained at provincial level as compared to country level.
Mixed Effects Model, Panel Data, Crime Rate, Kenya, Provinces
To cite this article
Chris Muchwanju, Joel Cheruyiot Chelule, Joseph Mung’atu, Modelling Crime Rate Using a Mixed Effects Regression Model, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 496-503. doi: 10.11648/j.ajtas.20150406.20
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Asteriou, Dimitrios; Hall, Stephen G. (2011). "Misspecification: Wrong Regressors, Measurement Errors and Wrong Functional Forms". Applied Econometrics (Second ed.). London: Palgrave MacMillan. pp. 172–197.
Becker, G. (1968). Crime and Punishment: An Economic Approach. The Journal of Political Economy,76/2 , 169-217.
Brooks, Chris (2014). Introductory Econometrics for Finance (3rd Ed.). Cambridge: Cambridge University Press. p. 461. ISBN 9781107661455.
C.Cornwell and N.Trumbul. (1994). Estimating the Economic Model of Crime with panel Data. The Review of Economics and Statistics,Vol.76.No.2(May,1994), 360-366.
Ehrlich. (1999). Crime,Punishement,and the Market for Offenses. The Journal of Economic Perspectives, Vol.10.1, 43-67.
Entorf and Spengler. (2002). Crime in Europe: Causes and Consequences. Springer.
Gelman, A. and J. Hill. Data Analysis Using Regression and Multilevel/Hierarchical Models. New York, NY: Cambridge University Press, 2007.
Gujarati, Damodar N.; Porter, Dawn C. (2009). "Panel Data Regression Models". Basic Econometrics (Fifth international ed.). Boston: McGraw-Hill.
Hosmer, David (2013). Applied logistic regression. Hoboken, New Jersey: Wiley. ISBN 978-0470582473.
Howell, David C. (2010). Statistical Methods for Psychology, 7th ed. Belmont, CA; Thomson Wadsworth. ISBN 978-0-495-59786-5.
Levitt, S. (1996). The Effect of Prison Population Size on Crime Rates: Evidence from Prison Overcrowding Litigation. The Quarterly JOurnal of Economics,111/2, 319-351.
Marselli and Vannini. (1997). Estimating a Crime Equation in the Presence of Organized Crime:Evidence from Italy. International Review of Law and Economics 17, 89-113.
Schafer. (1976). Fear of Crime and Criminal Victimizations:Gender-based Contrasts. Journal of Criminal Justice,Vol.34, 285-301.
Zuur, A. F., Ieno, E. N., Walker, N., Saveliev, A. a., & Smith, G. M. (2009). Mixed effects models and extensions in ecology with R. Statistics. New York, NY: Springer. doi:10.1007/978-0-387-8745.
Levit, S.(2001). Alternative startegies for Identifying the Link between Unemployment and Crime. Journal of Quantitative Criminology, 17/4,377-390.
Orsagh. (1979). Empirical Criminology: Interpreting Results Derived From Aggregate Data. Journal Of Research in Crime and Deliquency, 294-306.
Witte, A. D. (1980). Estimating the Economics Model of Crime with Individual Data. The quarterly journal of economics, Vol. 94, No. 1., 57-84.
Ehrlich, I. (1973). Participation in Illegitimate Activities: A Theoretical and Empirical Investigation. The Journal of POlitical Economy,81/3, 521-565.
Becker, G. (1993). Noble Lecture: The economic way of looking at behaviour. Journal of political econmy 101, 385-409.
Baltagi and Akom. (1990). On Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variables Estimators. Journal of Applied Econometrics, Vol.5,No.4, 401-406.John Wiley & Sons.
Andreoni. (1991). Reasonable Doubt and Optimal magnitude of fines: should the punishment fit crime? RAND Journal of Economics, 22 (3), 385-395.
Bryk, A.S. and S.W. Raudenbush (1992) Hierarchical Linear Models, Applications and Data Analysis Methods. Newbury Park, CA: Sage.
Raudenbush, s. W., Bryk, A. s., Cheong, Y. F., Congdon, R., & Du Toit, M. (2011). HLM 7: Hierarchical linear and nonlinear modeling. Lincolnwood, IL: scientific software International.
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