mag_ctrl: After removing control variables, magnitude of effect of x on... In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

Description

Uses Vinod (2015) and runs kernel regressions: x~ y + ctrl and x~ ctrl to evaluate the ‘incremental change’ in R-squares. Let (rxy;ctrl) denote the square root of that ‘incremental change’ after its sign is made the same as that of the Pearson correlation coefficient from cor(x,y)). One can interpret (rxy;ctrl) as a generalized partial correlation coefficient when x is regressed on y after removing the effect of control variable(s) in ctrl. It is more general than the usual partial correlation coefficient, since this one allows for nonlinear relations among variables. Next, the function computes ‘dxdy’ obtained by multiplying (rxy;ctrl) by the ratio of standard deviations, sd(x)/sd(y). Now our ‘dxdy’ approximates the magnitude of the partial derivative (dx/dy) in a causal model where y is the cause and x is the effect. The function also reports entirely analogous ‘dydx’ obtained by interchanging x and y.

Usage

 1 mag_ctrl(x, y, ctrl)

Arguments

 x Vector of data on the dependent variable. y Vector of data on the regressor. ctrl data matrix for designated control variable(s) outside causal paths. A constant vector is not allowed as a control variable.

Value

vector of two magnitudes ‘dxdy’ (effect when x is regressed on y) and ‘dydx’ for reverse regression. Both regressions remove the effect of control variable(s).

Note

This function is intended for use only after the causal path direction is already determined by various functions in this package (e.g. someCPairs). That is, after the researcher knows whether x causes y or vice versa. The output of this function is a vector of two numbers: (dxdy, dydx), in that order, representing the magnitude of effect of one variable on the other. We expect the researcher to use only ‘dxdy’ if y is the known cause, or ‘dydx’ if x is the cause. These approximate overall measures may not be well-defined in some applications, because the real partial derivatives of nonlinear functions are generally distinct for each evaluation point.

Author(s)

Prof. H. D. Vinod, Economics Dept., Fordham University, NY

References

Vinod, H. D. 'Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, doi: gffn86

Vinod, H. D. 'Matrix Algebra Topics in Statistics and Economics Using R', Chapter 4 in Handbook of Statistics: Computational Statistics with R, Vol.32, co-editors: M. B. Rao and C. R. Rao. New York: North Holland, Elsevier Science Publishers, 2014, pp. 143-176.