Individual tree height increment model for managed even-aged stands of ponderosa pine throughout the western United States using linear mixed effects models

A height increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in western United States. The data set used in this study came from long-term permanent research plots in even-aged, pure stands both planted and of natural origin. The data base consists of six levels-of-growing stock studies supplemented by initial spacing and other permanent-plot thinning studies for a total of 310 plots, 34,263 trees and 122,082 observations. Regression analysis is the most commonly used statistical method in forest modeling. However, research studies with repeated measurements are common in forestry and other biological disciplines. We choose the mixed models instead of the regression analysis approach because it allows for proper treatment of error terms in a repeated measures analysis. The model is well behaved and possessed desirable statistical properties. Our goal is to present a single height increment model applicable throughout the geographic range of ponderosa pine in the United States and by using only data from long-term permanent plots on sites capable of the productivity estimated by Meyer [Meyer, W.H., 1938. Yield of Even-aged Stands of Ponderosa Pine. US Department of Agriculture Technical Bull. 630].