Using error-in-variable regression to predict tree diameter and crown width from remotely sensed imagery

Automated individual tree detection and delineation from high spatial resolution imagery provides good opportunities for forest inventory at a large scale. However, the accuracy of delineated crown size compared with ground measurements may not be sufficient. Thus, ordinary least squares (OLS) regression is no longer an appropriate approach to estimating and predicting variables from the delineated tree crown because both response variable and regressor are subject to measurement errors. In this study, we describe the functional and structural relationships between field-measured tree variables (i.e., tree diameter and crown width) and delineated tree crown width from remotely sensed imagery. We investigated the performance of OLS and three error-in-variable regression techniques including maximum likelihood estimator (MLE), major axis (MA) regression, and reduced major axis (RMA) regression using field-measured data and simulated data under different conditions. Our results indicated that MLE was desirable for estimating unbiased model coefficients. However, the adjustment assumption of the MLE model should be checked for predicting tree variables from remotely sensed imagery. When the assumption holds, the MLE model performed better for predicting the response variables than did the OLS model. Otherwise, the MLE model produced biased predictions for the response variables.