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