New and established regression techniques to address design-bias trends in fixed populations

In many studies applying remotely sensed data and regression analysis for assessing ecosystem characteristics, such as biomass or growing stock volume in forests, a trend from over-predicting small true values to under-predicting large true values is observed. The reason for this trend often remains elusive, but it can be shown that it is a direct consequence of, deliberately or by mistake, adopting a design-based inference perspective when evaluating the results from model-based predictions. However, the design-bias trend is problematic in many applications, because the real conditions within the ecosystem studied will not be correctly determined. Instead, predictions tend to be shrunk towards the mean value of the target variable in the sample data used for estimating the parameters of the prediction model. Thus, calibration techniques to mitigate the design-bias trend have been proposed by some authors. In this article, we evaluate various regression techniques with respect to bias. The method of evaluation is founded on design-based inference, and thus, with regard to terminology, the regression techniques are used for estimating fixed quantities at the level of population elements rather than for predicting random quantities, as in the case of model-based inference. With aerial laser scanning data or digital aerial photographs, standard ordinary least squares (OLS) regression combined with classical calibration (CC) and the new MAVGAR method performed best in terms of bias, and produced good or reasonably good root mean square error (RMSE) values. The MAVGAR method aims to minimize the mean of the absolute values of groupwise average residuals, which is the origin of its name. None of the evaluated methods performed well in producing estimates with low bias when optical satellite data were used.