Last modified: 2018-05-18

#### Abstract

Regression splines, based on piecewise polynomial, are useful tools to model departures from linearities in the regression context. The number and location of the knots can be of interest in many context since they can detect possible change points in the relationship between the variables. Nonetheless, in literature, little research had been done on this topic and the interest is mainly in selecting a smooth curve to describe the relationship. This work is focused on the estimate of both number and location of knots in the simple case where linear truncated spline are chosen to represent the realtionship, in this case the position of the knot detects a change in the slope. In a Bayesian context, we propose a two-step procedure, to first determine the true number of knots and then to fit the final model estimating simultaneously knots location, regression and spline coefficients.