sudoCoefParcorH function

Peudo regression coefficients from hybrid generalized partial correlation coefficients (HGPCC).

This function gets HGPCCs by calling parcorVecH function. Pseudo regression coefficient of a kernel regression is obtained by HGPCC*(sd dep.var)/(sd regressor), that is multiplying the HGPCC by the standard deviation (sd) of the dependent variable and dividing by the sd of the regressor.

sudoCoefParcorH(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

Hybrid Generalized Partial Correlation Coefficients (HGPCC) allow comparison of the relative contribution of each $X_j$ to the explanation of $X_i$, because GPCC are scale-free. Hybrid refers to use of OLS residuals. Now pseudo hybrid regr coeff are HGPCC*(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
sudoCoefParcorH(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.