A Flexible Height-Diameter Model for Tree Height Imputation on Forest Inventory Sample Plots Using Repeated Measures from the Past

In this study, height-diameter relations were modeled using two different mixed model types for imputation of missing heights from longitudinal data. Model Type A had a hierarchical structure of sample plot-specific and measurement occasion-specific random effects. In Model Type B, a possible temporal variance was modeled by a sample plot-specific linear time trend. Furthermore, various calibration strategies of random effects were performed on past and current data, and a combination of both. The performance of the mixed models was compared on independent data using bias and root mean square error (RMSE). The results showed that Model Type A achieved the highest precision (lowest RMSE), if sample plot-specific random effects were predicted from old data and measurement occasion-specific ones were predicted from new data. In comparison, however, Model Type B had a higher RMSE, and lower bias. Model performance was almost unaffected from the usage of past or current data for the prediction of random effects. Results revealed that a certain calibration strategy should be simultaneously applied to all random effects from the same hierarchy level. Otherwise, predictions would become imprecise and a serious bias may result. In comparison with traditional uniform height curves, the novel mixed model approach performed slightly better.