Determining one or more change points

Abstract

A statistical method is presented for determining whether a line has one or more change points at unknown locations. A change point is a point where a line suddenly changes its slope but is continuous, i.e. it does not jump. Change points are also referred to as break points or join points. A step-wise procedure is suggested which starts by fitting a straight line without change points. Next a line with a single change point is fit to the data, and a statistical test is used to determine if the line with a single change point provides a significantly better fit to the data than the line with no change points. This can then be followed by fitting a line with two change points, etc. The problem of determining the number of change points that best fits the data is discussed. A modified version of Akaike's information criterion (AIC) is used to select the best number of change points to avoid over fitting. An example of fluorescence anisotropy measurements of the total phospholipid from the liver of a marine fish as a function of temperature is presented. Keywords: Change points; Break points; Statistical methods; Join points; Linear splines