This study assesses univariate and multivariate spatial regression models for predicting individual tree structure variables using Light Detection And Ranging (LiDAR) covariates. Many studies have used covariates derived from LiDAR to help explain the variability in tree, stand, or forest variables at a fine spatial resolution across a specified domain. Few studies use regression models capable of accommodating residual spatial dependence between field measurements. Failure to acknowledge this spatial dependence can result in biased and perhaps misleading inference about the importance of LiDAR covariates and erroneous prediction. Accommodating residual spatial dependence, via spatial random effects, helps to meet basic model assumptions and, as illustrated in this study, can improve model fit and prediction. When multiple correlated tree structure variables are considered, it is attractive to specify joint models that are able to estimate the within tree covariance structure and use it for subsequent prediction for unmeasured trees. We capture within tree residual covariances by specifying a model with multivariate spatial random effects. The univariate and multivariate spatial random effects models are compared to those without random effects using a data set collected on the U.S. Forest Service Penobscot Experimental Forest, Maine. These data comprise individual tree measurements including geographic position, height, average crown length, average crown radius, and diameter at breast height.