A Bayesian piecewise linear model for the detection of breakpoints in housing prices

Statistical thresholds occur when the changes in the relationships between a response and predictor variables are not linear but abrupt at some points of the predictor variable values. In this paper, we defined a piecewise-linear regression model which can detect two thresholds in the relationships via changes in slopes. We developed the corresponding Bayesian methodology for model estimation and inference by proposing prior distributions, deriving posterior distributions, and generating posterior values using Metropolis and Gibbs sampling algorithm. The parameters in our model are easy to understand, highly interpretable, and flexible to make inferences. The methodology has been applied to estimate threshold effects in housing market pricing data in two cities - Kamloops and Chilliwack - in British Columbia, Canada. Our findings revealed that the implementation of changes in the government property tax policies had threshold effects in the market price trend. The proposed model will be useful to detect threshold effects in other correlated time series data as well.