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Partial Derivative dy/d_[wrt]

Source: R/dy_d_wrt.R
dy.d_.Rd

Returns the numerical partial derivative of y with respect to [wrt] any regressor for a point of interest. Finite difference method is used with NNS.reg estimates as f(x + h) and f(x - h) values.

Usage

dy.d_(x, y, wrt, eval.points = "obs", mixed = FALSE, messages = TRUE)

Arguments

x

a numeric matrix or data frame.

y

a numeric vector with compatible dimensions to x.

wrt

integer; Selects the regressor to differentiate with respect to (vectorized).

eval.points

numeric or options: ("obs", "apd", "mean", "median", "last"); Regressor points to be evaluated.

  • Numeric values must be in matrix or data.frame form to be evaluated for each regressor, otherwise, a vector of points will evaluate only at the wrt regressor. See examples for use cases.

  • Set to (eval.points = "obs") (default) to find the average partial derivative at every observation of the variable with respect to for specific tuples of given observations.

  • Set to (eval.points = "apd") to find the average partial derivative at every observation of the variable with respect to over the entire distribution of other regressors.

  • Set to (eval.points = "mean") to find the partial derivative at the mean of value of every variable.

  • Set to (eval.points = "median") to find the partial derivative at the median value of every variable.

  • Set to (eval.points = "last") to find the partial derivative at the last observation of every value (relevant for time-series data).

mixed

logical; FALSE (default) If mixed derivative is to be evaluated, set (mixed = TRUE).

messages

logical; TRUE (default) Prints status messages.

Value

Returns column-wise matrix of wrt regressors:

  • dy.d_(...)[, wrt]$First the 1st derivative

  • dy.d_(...)[, wrt]$Second the 2nd derivative

  • dy.d_(...)[, wrt]$Mixed the mixed derivative (for two independent variables only).

Note

For binary regressors, it is suggested to use eval.points = seq(0, 1, .05) for a better resolution around the midpoint.

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)

Vinod, H. and Viole, F. (2020) "Comparing Old and New Partial Derivative Estimates from Nonlinear Nonparametric Regressions" doi:10.2139/ssrn.3681104

Author

Fred Viole, OVVO Financial Systems

Examples