Hierarchical segmented regression models with application to a wood density study

Wood density is an important characteristic of wood, and plays a major role in determining the strength of wood products. One quantity useful in calculating wood density is called area-increment, which is the estimate of the cross-sectional area of the last ring at a horizontal cut of a tree. The focus of this study is modeling of area increment as a function of a scaled measurement of the tree-height at which area increment was determined from samples taken at various heights of 60 lodgepole pine trees in British Columbia, Canada. The relationship between area increment and scaled tree height is approximated by a hierarchical segmented regression model. Slopes of the segments vary over trees in this mixed-effect modeling framework. Maximum likelihood estimation is performed for inference concerning the model parameters and the model is assessed using a variety of techniques.