Package 'curvir'

Reserve demand curve

Description

Fits the reserve demand curve between excess reserves and normalised rates

Usage

curve(x, y, type = "logistic", dummy = NULL, q = NULL, ...)

Arguments

x	A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional).
y	A vector of normalised interest rates.
type	The type of the reserve demand curve. This can be any of logistic, redLogistic, fixLogistic, doubleExp, exponential, fixExponential, arctan, linear. See details in curve
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.
q	Target interval. This is a scalar below 1, for example 0.9 is the 90% interval. If NULL then no quantiles are estimated.
...	Additional arguments passed to optimiser curveopt.

Details

For a description of the parametric curves, see the provided reference. Below we list their functions:

• logisitc (Logistic)

  $r_i = \alpha + \kappa / (1 - \beta e^{g(\bm{C}_i)}) + \varepsilon_i$

• redLogistic (Reduced logistic)

  $r_i = \alpha + 1 / (1 - \beta e^{g(\bm{C}_i)}) + \varepsilon_i$

• fixLogistic (Fixed logistic)

  $r_i = \alpha + 1 / (1 - e^{g(\bm{C}_i)}) + \varepsilon_i$

• doubleExp (Double exponential)

  $r_i = \alpha + \beta e^{\rho e^{g(\bm{C}_i)}} + \varepsilon_i$

• exponential (Exponential)

  $r_i = \alpha + \beta e^{g(\bm{C}_i)} + \varepsilon_i$

• fixExponential (Fixed exponential)

  $r_i = \beta e^{g(\bm{C}_i)} + \varepsilon_i$

• arctan (Arctangent)

  $r_i = \alpha + \beta \arctan ( g(\bm{C}_i)) + \varepsilon_i$

• linear (Linear)

  $r_i = g(\bm{C}_i) + \varepsilon_i$

And $g(\bm{C}) = c + \bm{C} w_g$, where $\alpha$, $\beta$, $\kappa$, $\rho$ are curve parameters, $c$ is a constant togglable by constant, $\bm{C}$ are the regressors including the excess reserves. $w_g$ their coefficients, and finally $\varepsilon_i$ is the error term of the curve.

Value

Returns a model of class curvir. This includes

• type the type of the curve.

• constant a logical indicating the use of a constant.

• w a list including: mean the curve parameters for the mean of the curve, upper and lower the parameters for the curve at the upper and lower intervals.

• data a list including the y, x, and dummy used for the fitting of the curve.

• mse the MSE from the fitting of the curve (the mean only).

• q the interval used in the fitting of the curve.

Note

An additional column for the constant is automatically generated, unless requested otherwise.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

predict.curvir, plot.curvir, and curveopt.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1,drop=FALSE]
  curve(x,rate)

  # An arctangent curve
  curve(x,rate,type="arctan")

---

Optimise curve parameters

Description

Finds optimal curve parameters.

Usage

curveopt(
  x,
  y,
  type = "logistic",
  constant = c(TRUE, FALSE),
  reps = 3,
  sign = NULL,
  q = NULL,
  winit = NULL,
  yhat = NULL,
  wsel = c("select", "combine"),
  dummy = NULL,
  sameSign = c(TRUE, FALSE)
)

Arguments

x	A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional).
y	A vector of normalised interest rates.
type	The type of the reserve demand curve. This can be any of logistic, redLogistic, fixLogistic, doubleExp, exponential, fixExponential, arctan, linear. See details in curve
constant	A logical (TRUE or FALSE) whether to include a constant or not.
reps	Number of repetitions for the particle swarm optimisation.
sign	A vector of equal length to the number of additional regressors in x (excluding the constant (if used) and the excess reserves) of positive and negative values (any) that will be used to obtain signs to restrict the values of the estimated parameters. Use NULL for no restrictions.
q	The desired quantile to optimise for. Use NULL to get the conditional expectation.
winit	A vector of initial values for the optimisation. This will also carry over to sign restrictions if sameSign==TRUE.
yhat	Useful when estimating quantiles. Supply here the predicted values for the conditional expectation to add restrictions for the quantiles to not cross the conditional expectation. Use NULL to not add any restrictions.
wsel	Use the minimum error set of parameters (select) or the combination of the pool parameters using the heuristic in Kourentzes et al., (2019) (combine).
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.
sameSign	Used if winit != NULL to take any sign restrictions from winit.

Value

Returns a list of

• w The optimal parameters

• mse The Mean Squared Error of the fitted curve.

Author(s)

Nikolaos Kourentzes, [email protected]

References

• Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

• Kourentzes, N., Barrow, D., & Petropoulos, F. (2019). Another look at forecast selection and combination: Evidence from forecast pooling. International Journal of Production Economics, 209, 226-235.

See Also

curve, and curvepred.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1,drop=FALSE]
  curveopt(x,rate)

---

Reserve demand curve predicted values

Description

Provides the predicted values for the reserve demand curve of choice. For general use prefer the predict() function, which handles the constant internally.

Usage

curvepred(x, w, type = "logistic", dummy = NULL)

Arguments

x	A matrix with the inputs. If there is a constant in the estimated curve, then the first column in x should be the constant. Next column should be the excess reserves. Additional regressor follow (optional).
w	The vector of weights for the desired curve. Estimated using the curveopt function.
type	The type of the reserve demand curve. This can be any of logistic, redLogistic, fixLogistic, doubleExp, exponential, fixExponential, arctan, linear. See details in curve
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.

Details

For a description of the parametric curves, see the provided reference. Below we list their functions:

• logisitc (Logistic)

  $r_i = \alpha + \kappa / (1 - \beta e^{g(\bm{C}_i)}) + \varepsilon_i$

• redLogistic (Reduced logistic)

  $r_i = \alpha + 1 / (1 - \beta e^{g(\bm{C}_i)}) + \varepsilon_i$

• fixLogistic (Fixed logistic)

  $r_i = \alpha + 1 / (1 - e^{g(\bm{C}_i)}) + \varepsilon_i$

• doubleExp (Double exponential)

  $r_i = \alpha + \beta e^{\rho e^{g(\bm{C}_i)}} + \varepsilon_i$

• exponential (Exponential)

  $r_i = \alpha + \beta e^{g(\bm{C}_i)} + \varepsilon_i$

• fixExponential (Fixed exponential)

  $r_i = \beta e^{g(\bm{C}_i)} + \varepsilon_i$

• arctan (Arctangent)

  $r_i = \alpha + \beta \arctan ( g(\bm{C}_i)) + \varepsilon_i$

• linear (Linear)

  $r_i = g(\bm{C}_i) + \varepsilon_i$

And $g(\bm{C}) = c + \bm{C} w_g$, where $\alpha$, $\beta$, $\kappa$, $\rho$ are curve parameters, $c$ is a constant togglable by constant, $\bm{C}$ are the regressors including the excess reserves. $w_g$ their coefficients, and finally $\varepsilon_i$ is the error term of the curve.

Value

Returns a vector of the predicted values.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

curve, and curveopt.

---

curvir:Reserve demand curve modelling toolbox

Description

The curvir package provides tools for building reserve demand curves for central bank operations.

Parametric curve modelling

• curve - fit a parametric curve

• curveopt - optimise curve parameters (called through curve)

• curvepred - predict curve values (called through predict)

• invcurve - produce predictions from the inverse curve

Non-parametric curve modelling

• npcurve - fit a non-parametric curve

Curve specification

• cvfit - Joint automatic specification of curve type and regressors

• varselect - Automatic specification of regressors

• cvnpcurve - Provide cross-validated errors for non-paramteric curves

• cvfitplot - Summary plot for cvfit and cvnpcurve

General

• predict Predict parametric and non-parametric curves

• plot Plot parametric and non-parametric curves

Data

• ecb ECB dataset from Chen et al. (2023)

Author(s)

Nikolaos Kourentzes, [email protected], Zhuohui Chen, [email protected], Romain R. Veyrune.

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

---

Automatically select curve type and explanatory variables

Description

Using cross-validation automatically select explanatory variables jointly with curve type. When running cvfit there is no need to use varselect separately.

Usage

cvfit(
  x,
  y,
  folds = 10,
  constant = c(TRUE, FALSE),
  sign = NULL,
  reps = 3,
  parallel = c(FALSE, TRUE),
  usepbapply = c(FALSE, TRUE),
  alltype = c("logistic", "redLogistic", "doubleExp", "exponential", "arctan", "linear"),
  search = c("backward", "forward"),
  wsel = c("select", "combine"),
  dummy = NULL
)

Arguments

x	A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional).
y	A vector of normalised interest rates.
folds	Folds to use for cross-validation.
constant	A logical (TRUE or FALSE) whether to include a constant or not.
sign	A vector of equal length to the number of additional regressors in x (excluding the constant (if used) and the excess reserves) of positive and negative values (any) that will be used to obtain signs to restrict the values of the estimated parameters. Use NULL for no restrictions.
reps	Number of repetitions for the particle swarm optimisation.
parallel	Initialise and use parallel processing for the cross-validation. Note that the maximum number of cores that will be used is equal to the alternative types of curves that are evaluated (alltype).
usepbapply	A logical to indicate whether to use pbapply to report on the parallel calculation progress. Note that pbapply does not support load balancing.
alltype	A vector of the curve types to consider in the selection process.
search	Search strategy for variable inclusion. With forward the model starts from no explanatory variables, and evaluates potential additions. With backward the model starts with all variables and evaluates for potential exclusions.
wsel	Use the minimum error set of parameters (select) or the combination of the pool parameters using the heuristic in Kourentzes et al., (2019) (combine).
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.

Value

Returns a list with the recommended variable selection choice:

• type the type of selected curve.

• keep a logical vector with which variables to keep.

• varRes the result from varselect for each evaluated curve type.

• cvIndex a matrix detailing how the sample was split for the cross-validation. First column is the fold number and second column is the index of the observation.

Use cvfitplot to visualise the output.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

cvfitplot, curve, and varselect.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1:3,drop=FALSE]
  cvKeep <- cvfit(x,rate,folds=5,alltype=c("logistic","arctan"),parallel=TRUE)
  # Print result
  print(cvKeep)
  # Fit curve with the selected variables
  curve(x[,cvKeep$keep,drop=FALSE],rate,type=cvKeep$type)

---

Plot output of cvfit to facilitate comparison

Description

Plot summarised error of different curves specification from cvfit. Assuming normal errors, plot the mean cross-validated error and the 95

Usage

cvfitplot(cvKeep, xlock = c("mean", "median"), cvRF = NULL, cvSP = NULL)

Arguments

cvKeep	The output of cvfit.
xlock	Focus horizontal axis on mean or median, The latter provides a narrower range, facilitating comparison when there are outliers.
cvRF	Include cross-validation results from random forecast non-parametric curves. Obtain these from cvnpcurve with type="rforest". Use NULL to ignore.
cvSP	Include cross-validation results from spline regression non-parametric curves. Obtain these from cvnpcurve with type="spline". Use NULL to ignore.

Value

No returned value. Produces a summary plot of cross-validated errors.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

cvfit.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1:3,drop=FALSE]
  cvKeep <- cvfit(x,rate,folds=5,alltype=c("logistic","arctan"),parallel=TRUE)
  cvfitplot(cvKeep)
  # Add results from non-parameteric curves
  cvRF <- cvnpcurve(x,rate,cvKeep$cvIndex)
  cvSP <- cvnpcurve(x,rate,cvKeep$cvIndex,type="spline")
  cvfitplot(cvKeep,cvRF=cvRF,cvSP=cvSP)

---

Cross-validated errors for non-parametric curve

Description

Obtain cross-validated errors for a non-parametric curve with given sample splits.

Usage

cvnpcurve(x, y, cvIndex, type = "rforest", dummy = NULL)

Arguments

x	A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional).
y	A vector of normalised interest rates.
cvIndex	A matrix detailing how the sample was split for the cross-validation. Output from cvfit.
type	The type of the reserve demand curve. This can be any of rforecast for random forecast or spline for spline regression.
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.

Value

Returns summary cross-validated errors, comparable with the output from cvfit.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

cvfit, and cvfitplot.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1:3,drop=FALSE]
  cvKeep <- cvfit(x,rate,folds=5,alltype=c("logistic","arctan"),parallel=TRUE)
  # Get non-parametric curve cross-validated errors
  cvRF <- cvnpcurve(x,rate,cvKeep$cvIndex)
  cvSP <- cvnpcurve(x,rate,cvKeep$cvIndex,type="spline")

---

ECB excess reserve data

Description

The short-term interest rate used for the European Central Bank (ECB) is the volume-weighted Euro Overnight Index Average (EONIA) rate. Various explanatory variables are provided, as listed in the Chen et al. (2023). Data are collected from 1999 to 2019, resulting in 239 maintenance periods where all data is available.

Usage

ecb

Format

ecb a list containing

• rate the normalised EONIA rate.

• x a matrix including the ECB excess reserves and various regressors.

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

Examples

plot(ecb$x[,1],ecb$rate,xlab="Excess Reserves",ylab="Rate")

---

Calculate the inverse curve prediction

Description

Calculate the predicted reserves given some rate, i.e., calculate the prediction of the inverse curve.

Usage

invcurve(
  object,
  ynew = NULL,
  xnew = NULL,
  dummynew = NULL,
  warn = c(TRUE, FALSE)
)

Arguments

object	A model fit with curve.
ynew	The input rate. If NULL this corresponds to the values from predict(object).
xnew	The values for the additional regressors that were used in the curve fit. Must be a matrix, ordered (columns) as they were input in the fitting of the curve. The constant is dealt with automatically. Do not input the excess reserves. If NULL this is picked up from the data used to fit the curve.
dummynew	The values for the indicator, if one was used in the fitting of the curve. If NULL then the data used in the fitting of the model are used.
warn	A logical (TRUE or FALSE) to issue a warning if the resulting values are more than 10% away from the min-max of the excess reserves used to estimate the curve.

Value

Returns a vector of values of the predicted reserves

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

curve, and predict.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1,drop=FALSE]
  fit <- curve(x,rate,type="logistic")
  invcurve(fit)

  # Use a different input rate
  invcurve(fit,ynew=0.1)

---

Reserve demand non-parametric curve

Description

Fits a non-parametric reserve demand curve between excess reserves and normalised rates

Usage

npcurve(x, y, type = c("rforest", "spline"), dummy = NULL, q = NULL, ...)

Arguments

x	A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional).
y	A vector of normalised interest rates.
type	The type of the reserve demand curve. This can be any of rforecast for random forecast or spline for spline regression.
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.
q	Target interval. This is a scalar below 1, for example 0.9 is the 90% interval. If NULL then no quantiles are estimated.
...	Additional arguments (unused).

Value

Returns a model of class npcurvir. This includes

• type the type of the curve.

• fit the non-parametric model for the mean.

• fitQ The non-parametric model for the quantiles.

• data a list including the y, x, and dummy used for the fitting of the curve.

• q the interval used in the fitting of the curve.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

predict.npcurvir, and plot.npcurvir.

Examples

# Use ECB example data
rate <- ecb$rate
x <- ecb$x[,1,drop=FALSE]
npcurve(x,rate)

---

Plot method for curvir reserve demand models

Description

Plot a reserve demand curve estimated using curve.

Plot a non-parametric reserve demand curve estimated using npcurve.

Usage

## S3 method for class 'curvir'
plot(
  x,
  ploty = c(FALSE, TRUE),
  plotq = c(TRUE, FALSE),
  usemean = c(FALSE, TRUE),
  prcmp = c(FALSE, TRUE),
  useline = c(FALSE, TRUE),
  main = NULL,
  pch = 20,
  ...
)

## S3 method for class 'npcurvir'
plot(
  x,
  ploty = c(FALSE, TRUE),
  plotq = c(TRUE, FALSE),
  usemean = c(FALSE, TRUE),
  prcmp = c(FALSE, TRUE),
  useline = c(FALSE, TRUE),
  main = NULL,
  pch = 20,
  ...
)

Arguments

x	A model fit with curve.
ploty	Logical (TRUE or FALSE) to plot data used for fitting or not.
plotq	Logical (TRUE or FALSE) to plot intervals.
usemean	Logical (TRUE or FALSE) to replace all explanatory variables (except from excess reserves) with their mean. It cannot be used if a dummy is used in the fitting of the curve.
prcmp	Logical (TRUE or FALSE) to use principal components to project all variables into two dimensions. Requires usemean == FALSE. This may be useful when multiple explanatory variables are used.
useline	Logical (TRUE or FALSE) to force line plots when usemean == FALSE or prcomp == FALSE and there are many explanatory variables.
main	Use to overide the default plot title.
pch	Use to overide the dafault marker type for points.
...	Additional inputs (currently unused).

Value

No returned value. Produces a plot of the estimated curve.

Methods (by class)

• plot(curvir): Plot parametric curves

• plot(npcurvir): Plot non-parametric curves

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

curve.

npcurve.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1,drop=FALSE]
  fit <- curve(x,rate)
  plot(fit)


# Use ECB example data
rate <- ecb$rate
x <- ecb$x[,1,drop=FALSE]
fit <- npcurve(x,rate)
plot(fit)

---

Predict method for curvir reserve demand models

Description

Predicted values based on curvir model object

Predicted values based on npcurvir model object

Usage

## S3 method for class 'curvir'
predict(object, newdata = NULL, newdummy = NULL, ...)

## S3 method for class 'npcurvir'
predict(object, newdata = NULL, newdummy = NULL, ...)

Arguments

object	A model fit with npcurve.
newdata	New input data organised as the x matrix in curve. If NULL then the data used to fit the model is re-used.
newdummy	New input dummy organised as the dummy vector in curve. If NULL then the dummy used to fit the model is re-used.
...	Further arguments (unused)

Value

Returns a matrix of predicted values. If the model has estimates for intervals then it will provide upper and lower intervals.

Returns a matrix of predicted values. If the model has estimates for intervals then it will provide upper and lower intervals.

Methods (by class)

• predict(curvir): Predicted values for parametric curves

• predict(npcurvir): Predicted values for non-parametric curves

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

curve.

npcurve.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1,drop=FALSE]
  fit <- curve(x,rate)
  predict(fit)

  # An example with new data
  predict(fit,newdata=tail(x))
 

# Use ECB example data
rate <- ecb$rate
x <- ecb$x[,1,drop=FALSE]
fit <- npcurve(x,rate)
predict(fit)

---

Automatically select explanatory variables for a curve type

Description

Using cross-validation automatically select explanatory variables for a reserve demand curve type.

Usage

varselect(
  x,
  y,
  type = "logistic",
  folds = 10,
  constant = c(TRUE, FALSE),
  sign = NULL,
  reps = 3,
  search = c("backward", "forward"),
  wsel = c("select", "combine"),
  dummy = NULL
)

Arguments

x	A matrix of explanatory variables. Excess reserve must be the first input.Additional regressor follow (optional).
y	A vector of normalised interest rates.
type	The type of the reserve demand curve. This can be any of logistic, redLogistic, fixLogistic, doubleExp, exponential, fixExponential, arctan, linear. See details in curve
folds	Folds to use for cross-validation.
constant	A logical (TRUE or FALSE) whether to include a constant or not.
sign	A vector of equal length to the number of additional regressors in x (excluding the constant (if used) and the excess reserves) of positive and negative values (any) that will be used to obtain signs to restrict the values of the estimated parameters. Use NULL for no restrictions.
reps	Number of repetitions for the particle swarm optimisation.
search	Search strategy for variable inclusion. With forward the model starts from no explanatory variables, and evaluates potential additions. With backward the model starts with all variables and evaluates for potential exclusions.
wsel	Use the minimum error set of parameters (select) or the combination of the pool parameters using the heuristic in Kourentzes et al., (2019) (combine).
dummy	Optional input to signify a regime change (vertical shifts in the curve). Must be a vector of equal length to the rows of x. If not needed use NULL.

Value

Returns a list with the recommended variable selection choice:

• keep a logical vector with which variables to keep.

• errors statistics of the cross-validated MSE error.

Author(s)

Nikolaos Kourentzes, [email protected]

References

Chen, Z., Kourentzes, N., & Veyrune, R. (2023). Modeling the Reserve Demand to Facilitate Central Bank Operations. IMF Working Papers, 2023(179).

See Also

curve, and cvfit.

Examples

# Use ECB example data
  rate <- ecb$rate
  x <- ecb$x[,1:3,drop=FALSE]
  varKeep <- varselect(x,rate,folds=5)
  # Print result
  print(varKeep)
  # Fit curve with the selected variables
  curve(x[,varKeep$keep,drop=FALSE],rate)

---