Evaluation of structure specification in linear mixed models for modeling the spatial effects in tree height-diamater relationships


  • Junfeng Lu Lerfob, INRA, Nancy 54000, France
  • Lianjun Zhang Department of Forest and Natural Resources Management, State University of New York, College of Environmental Science and Forestry, One Forestry Drive, Syracuse, NY 13210, USA.




linear mixed model, spatial heterogeneity, spatial autocorrelation, height-diameter equation


In recent years, linear mixed models (LMM) have become more popular to deal with spatial effects in forestry and ecological data. In this study, different structure specifications of linear mixed model were applied to model tree height-diameter relationships, including LMM with random blocks only (LMM-block), LMM with spatial covariance only (LMM-covariance), and the combination of the last two (LMM-block-covariance). Further, the between-group heterogeneous variances were incorporated into LMM-covariance and LMM-block-covariance. The results indicated that, in general, LMM-covariance significantly reduced spatial autocorrelation in model residuals, while LMM-block was effective in dealing with spatial heterogeneity. LMM-block treated the blocks as random effects and avoided the estimation of parameters of the variogram model. Thus, it produced better model predictions than LMM-covariance. LMM-block-covariance took both block effects and spatial covariance into account, and significantly improve model fitting. However, it did not produce better model predictions due to the increase of model complexity and estimation of the local variogram within each block. 






Research article