parcorMtx function

Matrix of generalized partial correlation coefficients, always leaving out control variables, if any.

This function calls parcor_ijk function which uses original data to compute generalized partial correlations between $X_i$ and $X_j$

where j can be any one of the remaining variables in the input matrix mtx. Partial correlations remove the effect of variables $x_k$ other than $X_i$ and $X_j$. Calculation further allows for the presence of control variable(s) (if any) to remain always outside the input matrix and whose effect is also removed in computing partial correlations.

parcorMtx(mtx, ctrl = 0, dig = 4, verbo = FALSE)

Arguments

• mtx: Input data matrix with p columns. p is at least 3 columns.
• ctrl: Input vector or matrix of data for control variable(s), default is ctrl=0 when control variables are absent
• dig: The number of digits for reporting (=4, default)
• verbo: Make this TRUE for detailed printing of computational steps

Returns

A p by p `out' matrix containing partials r*(i,j | k). and r*(j,i | k).

Note

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)
parcorMtx(mtx)
 
   
## Not run:

set.seed(34);x=matrix(sample(1:600)[1:99],ncol=3)
colnames(x)=c('V1', 'v2', 'V3')
parcorMtx(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

See Also

See Also parcor_ijk.

Author(s)

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