A Non-Least-Squares Method for Estimation of Broken-Line Regression to Determine Plateau Time of Output in a Milk Production Study

• Activity Number: 525
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Greg Knofczynski*+ and Lorrie Hoffman
• Companies: Armstrong Atlantic State University and Armstrong Atlantic State University
• Keywords: change point ; joinpoint ; nonparametric

Abstract

Broken-line regression has been used to estimate parameters in increasing or decreasing linear trends that may plateau either initially or at a later point in time. Most approaches employ least squares methods that under usual assumptions lead to maximum likelihood estimates (Gill, 2004). In Hoffman, Knofczynski and Clark (2010) an estimation procedure called MMNPR is derived and simulation studies show that this method's parameter estimates of the broken-line regression perform better than the MLEs in small sample situations when data is from distributions where error terms are ill-behaved. A review of applied science literature revealed many studies using broken-line regression and we choose to extend the data analysis of one animal study that reports parameters based on least squares approaches for milk output of cows (Sahinler, 2009). We investigate the appropriateness of underlying assumptions concerning correlation and homoscedacity. We compute the plateau time and level using the MMNPR technique, discussing the differences between parameter estimates based on least squares and those based on the MMNPR technique from Hoffman, Knofczynski and Clark.