A Min.Max Algorithm for Spline Based Modeling of Violent Crime Rates in USA

TL;DR

This paper introduces a new min/max algorithm for knot detection in cubic spline regression to model violent crime rates in the US from 1960 to 2014, achieving high goodness-of-fit.

Contribution

The paper presents a novel min/max algorithm for knot detection in spline modeling, improving the accuracy of violent crime rate predictions.

Findings

42 out of 51 states had R_adj^2 > 90%

The model fits well across different states and overall US data

Proposes a unified spline-based approach for future crime rate modeling

Abstract

This paper focuses on modeling violent crime rates against population over the years 1960-2014 for the United States via cubic spline based method. We propose a new min/max algorithm on knots detection and estimation for cubic spline regression. We employ least squares estimation to find potential regression coefficients based upon the cubic spline model and the knots chosen by the min/max algorithm. We then utilize the best subsets regression method to aid in model selection in which we find the minimum value of the Bayesian Information Criteria. Finally, we report the $R_{adj}^{2}$ as a measure of overall goodness-of-fit of our selected model. Among the fifty states and Washington D.C., we have found 42 out of 51 with $R_{adj}^{2}$ value that was greater than $90\%$. We also present an overall model for the United States as a whole. Our method can serve as a unified model for violent crime rate over future years.