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In this model, X is an explanatory variable which cannot be observed directly, and X̃ is the observable substitute variable of X, where e is a measurement error, (phi (cdot)) is an unconditional known function.
Additional biomass analysis of above and below ground biomass on reserve partial wheels in close vicinity to the main plots will extend the allometric analyses to the root-shoot allometry and deliver total shoot mass, plant mass, and specific wood density, while present evaluations are based on tree volume as substitute variable.
In most cases, the use of one substitute variable did not greatly diminish the average concordance index of the complete model (Table 2).
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Furthermore, we use a function b(A, B) to substitute variables: (16) b (A, B ) = { A if B = 1 ¬ A, otherwise.
Among the other substitute variables crown surface area seems to be the best, even better than sapwood area at breast height.
Deciding that among those substitute variables, which can be assessed in a non-destructive way, crown surface area is the best choice to predict leaf area, we furthermore investigated if these estimations can be improved by adding additional variables.
The 13-variable index we identified includes specific measures that fall into each of these categories, but we note that substitute variables can be used in some cases with little overall effect on predictive performance.
The scale additive creates a compound or synthetic measure using substitute variables, with those variables that contribute more weight for each selected factor acting as representatives of related factors.
Furthermore, the test for the hypothesis that the slope does not deviate from 1, indicates that leaf area can be assumed proportional to all substitute variables, except for the sapwood area at breast height.
Rather, employers who cannot commit to more substantive terms will be forced to reduce the employment opportunities they have; meaning some employees would be substituting variable employment for none at all.
Dependent on the input, Function 16 defines if the substituted variable is negated.
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