sudoCoefParcor function

Pseudo regression coefficients from generalized partial correlation coefficients, (GPCC).

This function gets the GPCCs by calling the parcorVec function. The pseudo regression coefficient of a kernel regression is then obtained by [GPCC*(sd dep.var)/(sd regressor)], that is, by multiplying the GPCC by the standard deviation (sd) of the dependent variable, and dividing by the sd of the regressor.

sudoCoefParcor(mtx, ctrl = 0, verbo = FALSE, idep = 1)

Arguments

• mtx: Input data matrix with p (> or = 3) columns,
• ctrl: Input vector or matrix of data for control variable(s), default is ctrl=0, when control variables are absent
• verbo: Make this TRUE for detailed printing of computational steps
• idep: The column number of the dependent variable (=1, default)

Returns

A p by 1 `out' vector pseudo partial derivatives.

Note

Generalized Partial Correlation Coefficients (GPCC) allow comparison of the relative contribution of each $X_j$ to the explanation of $X_i$, because GPCC are scale-free. The pseudo regression coefficient are not scale-free since they equal GPCC*(sd dep.var)/(sd regressor)

We want to get all partial correlation coefficient pairs removing other column effects. Vinod (2018) shows why one needs more than one criterion to decide the causal paths or exogeneity.

Examples

set.seed(234)
z=runif(10,2,11)# z is independently created
x=sample(1:10)+z/10  #x is partly indep and partly affected by z
y=1+2*x+3*z+rnorm(10)# y depends on x and z not vice versa
mtx=cbind(x,y,z)
sudoCoefParcor(mtx, idep=2)
 
   
## Not run:

set.seed(34);x=matrix(sample(1:600)[1:99],ncol=3)
colnames(x)=c('V1', 'v2', 'V3')#some names needed
sudoCoefParcor(x)
## End(Not run)

References

Vinod, H. D. 'Generalized Correlations and Instantaneous Causality for Data Pairs Benchmark,' (March 8, 2015) https://www.ssrn.com/abstract=2574891

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.

Vinod, H. D. 'New Exogeneity Tests and Causal Paths,' (June 30, 2018). Available at SSRN: https://www.ssrn.com/abstract=3206096

Vinod, H. D. (2021) 'Generalized, Partial and Canonical Correlation Coefficients' Computational Economics, 59(1), 1--28.

See Also

See Also parcor_ijk.

See Also a hybrid version parcorVecH.

Author(s)

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