A Generalized Marginal and Mixed-Effect Models for Predicting Tree-Level Mortality with Unequal Measurement Intervals for Scots Pine in Finland

Abstract

Logistic regression has been used to model individual tree mortality. However, unequal measurement intervals limit the use of reasonable link functions. Although marginal and mixed-effects models have been used, a comparison of these models for predicting mortality in new stands is lacking. We developed models for predicting the mortality of Scots pine (Pinus sylvestris) trees in Finland. The modelling data comprised 44 thinning experiments (127,057 tree-level observations), and 50% of the experiments were randomly selected for model evaluation (43 experiments, 112,518 tree-level observations). A complementary log–log model was used to predict mortality probability based on tree and stand characteristics and thinning effects. The measurement period length was added as an offset variable. The marginal (population-average) and mixed models with random effects (site, plot, and year) were fitted and evaluated. The evaluation consisted of fit statistics, comparisons of predicted and observed mortality rates, and simulations using the Motti stand simulator. The mixed models clearly provided better statistical fits than the marginal model. The evaluation with the Motti simulator showed the most accurate prediction in terms of stem number (N) and stand basal area (G) when using the marginal model. All models, except the random year effect, resulted in maximum G values that remained at a reasonable level in the prolonged Motti simulations. The current survival model in the Motti simulator is based on a relative density index derived from the self-thinning line and provides good prediction accuracy. Based on the new BAL-based models, we recommend the marginal model as an option to the current model.