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    Measuring tree height is a time-consuming process. Often, tree diameter is measured and height is estimated from a published regression model. Trees used to develop these models are clustered into stands, but this structure is ignored and independence is assumed. In this study, hierarchical linear models that account explicitly for the clustered structure of the data are compared with model forms currently used in forestry. The data consist of 1433 Douglas firs from 99 Oregon stands measured in 2000, and an independent evaluation dataset of similar size measured in 2001. Overall model performance improved substantially if the stand random effect could be predicted: root mean squared error (RMSE) decreased from 4.91 m (current models) to less than 3.73 m (hierarchical model, 1 tree sampled). However, if the random effect could not be estimated, the improvement was small (RMSE 4.45 m). The within-stand relationship between height and diameter was different from that between stands. As a result, the random and fixed components of the model are confounded. A mixed model that did not account for this problem performed worse than the model that assumed an independent data structure.

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    Monleon, Vicente J. 2003. A hierarchical linear model for tree height prediction. In: 2003 Joint Statistical Meetings - Section on Statistics & the Environment: 2865-2869

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