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

 mag_ctrl R Documentation

## After removing control variables, magnitude of effect of x on y, and of y on x.

### 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

``````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, \Sexpr[results=rd]{tools:::Rd_expr_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.

See `mag`

### Examples

``````
set.seed(123);x=sample(1:10); z=runif(10); y=1+2*x+3*z+rnorm(10)
options(np.messages=FALSE)
mag_ctrl(x,y,z)#dx/dy=0.47 is approximately 0.5, but dy/dx=1.41 is not approx=2,

``````

generalCorr documentation built on May 1, 2023, 9:06 a.m.