A Multivariate Linear Mixed-Effects Model for the Generalization of Sample Tree Heights and Crown Ratios in the Finnish National Forest Inventory

Abstract

Abstract The aim of this article was to develop a prediction model that could use the geographically representative but locally sparse sample tree data of the Finnish National Forest Inventory (FNFI) efficiently and account for the correlation structures in these data when generalizing sample tree characteristics over tally trees by species. The sample tree characteristics modeled were tree height and the ratio of live crown length to tree height. These are needed for all FNFI tally trees to obtain their stem volumes and biomasses. As a result, a multivariate linear mixed-effects model with species-specific parameters designed for the multiresponse FNFI data was developed. The fixed parts of the two linear models of the simultaneous system consist of both tree and stand-level independent variables such as dbh, mensurable stand characteristics, and site quality indicators. Because of the hierarchically correlated data, the intercepts and the slopes (i.e., the coefficients associated with tree characteristics) in the two models were assumed to vary randomly over clusters and forest stands within them. The random coefficients were also associated with components for random species effects. The selected formulation of the random parts of the models makes it possible to obtain localized species-specific curves for clusters and forest stands even with one measured sample tree. The results show that the multivariate mixed-effects model with species-specific components is a stable, efficient predictor and well applicable to locally sparse but geographically representative data of the FNFI type.