Canadian Forest Service Publications

The challenge of estimating a residual spatial autocorrelation from forest inventory data. 2017. Magnussen, S., Breidenbach, J., Mauro, F. Can. J. For. Res. 47(11): 1557-1566.

Year: 2017

Issued by: Pacific Forestry Centre

Catalog ID: 38889

Language: English

Availability: PDF (request by e-mail)

Available from the Journal's Web site.
DOI: 10.1139/cjfr-2017-0247

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Estimates of stand averages are needed by forest management for planning purposes. In forest enterprise inventories supported by remotely sensed auxiliary data, these estimates are typically derived exclusively from a model that does not consider stand effects in the study variable. Variance estimators for these means may seriously underestimate uncertainty, and confidence intervals may be too narrow when a model used for computing a stand mean omits a non-trivial stand-effect in one or more of the model-parameters, a non-trivial spatial distance dependent autocorrelation in the model residuals, or both. In simulated sampling from 36 populations with stands of different sizes, and differing with respect to: i) the correlation between a study variable (Y) and two auxiliary variables (X); ii) the magnitude of stand effects in the intercept of a linear population model linking X to Y; and iii) a first-order autoregression in Y and X – we learned that none of the tested designs provided reliable estimates of the within-stand autocorrelation among model residuals. More reliable estimates were possible from stand-wide predictions of Y. The anticipated bias in an estimated autoregression parameter had a modest influence on estimates of variance and coverage of nominal 95% confidence intervals for a synthetic stand mean.

Plain Language Summary

Stand means of key forest inventory attributes are needed for forest management purposes. Increasingly these means are obtained with a model linking auxiliary remotely sensed variables to the target variable of interest. Due to modest sample sizes most stand means will be synthetic, i.e. entirely model dependent. It is therefore important that the sampling design allows estimation of random stand effects, and that efforts are made to ascertain whether a spatial autocorrelation in true model residuals warrants estimation. In this study we demonstrate that an estimation of the spatial autocorrelation in empirical residual errors may be both imprecise and biased. Fortunately, reliable estimates of the autocorrelation can be estimated from model expectations of the target variable. Since model expectations are available for all virtual plots in all stands of interest, the computation of a spatial autocorrelation can be fast and straightforward.