mag_ctrl | R Documentation |

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.

```
mag_ctrl(x, y, ctrl)
```

`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. |

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).

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.

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

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`

```
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,
```

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