Evaluation of rate trend patterns via segmented regression: Case study of crime rates of Pakistan

Abstract

In many practical regression-type problems, one uniform regression function to the data was found inappropriate, since the functional relationship between the response and the regressor(s) changes at certain points of regressors. These points are usually called break points or change points. In such situations, regression models are applied that are obtained by a piecewise definition of the regression function. Simply, by parts regression is used to detect an abrupt change of the response function at an increase or decrease of an influential factor, and named as segmented regression. Theoretical efforts have been made in the subject when parameters of a linear regression system obeying separate regimes. A case study concerning the crime rates in Pakistan is carried out by segmented regression approach as a comparative overview of linear regression approach and the segmented regression approach. Segmented regression approach was found to be more opposite than that of linear regression analysis on the basis of Bayesian information criteria and permutation test criteria. Key words: Change point, permutation test, rate trends, segmented regression.