The phrase "as an auxiliary variable" is correct and usable in written English.
It can be used in contexts related to statistics, research, or data analysis where an additional variable is introduced to assist in understanding or modeling a relationship.
Example: "In our study, we included age as an auxiliary variable to better analyze the effects of the treatment."
Alternatives: "as a supplementary variable" or "as an additional variable".
This is done by introducing a permutation of the data points as an auxiliary variable.
In this model, the topographic index is used as an auxiliary variable correlated with the soil storage capacity.
The velocity gradient is introduced as an auxiliary variable and the p-NS system is decomposed into a first order system including the projection of the nonlinear stress tensor components to the local discontinuous space.
The aims of the research were (i) to understand the relationship between γ-radiometric data and the clay content within the different complex GPGs and (ii) to predict the clay content from γ radiometry with a regional calibration based on the GPG as an auxiliary variable.
In a second study, the estimated spatial means of the Mean Highest Water table and Mean Lowest Water table of six map units were estimated by Stratified Simple Random Sampling in both phases in combination with the regression estimator that uses the starting depth of hydromorphic properties in the soil profile as an auxiliary variable.
A Soil Quality Index (SQI) was developed to comparatively assess six types of land use (Annual Crops, Perennial Crops, Grazing, Espinal, Dense Espinal and Native Forest); and finally, SQI was interpolated at landscape scale using the soil-adjusted vegetation index (SAVI) as an auxiliary variable.
The requirement for consensus is expressed as constraints where an auxiliary variable is introduced to facilitate parallel processing, and the resulting constrained optimization problem is solved under the Augmented Lagrangian framework.
As for actuator saturation problem, an auxiliary variable is introduced and accommodated by the disturbance observer.
At the t th iteration, the multi-block ADM with parallel splitting works as follows: Step 1: Updating an auxiliary variable q: q ( t + 1 ) = λ ( t ) + β ∑ i = 1 L D i θ i ( t ) − e, where q is an auxiliary variable, λ is a Lagrange multiplier, and β is a positive constant.
Let us define an auxiliary variable θ as the proportion of the transmit power assigned to the energy beamforming.
Following Schreuder et al. (1987), many double sampling estimators assume that, over the population as a whole, a linear regression model relates a target variable of interest (Y) to an auxiliary variable (X) as.
