parcorVecH2 | R Documentation |

This is a second version to be used when ‘parcorVecH’ fails. (H=hybrid). This hybrid version of parcorVec subtracting only linear effects but using generlized correlation between OLS residuals

```
parcorVecH2(mtx, dig = 4, verbo = FALSE, idep = 1)
```

`mtx` |
Input data matrix with p (> or = 3) columns, first column must have the dependent variable |

`dig` |
The number of digits for reporting (=4, default) |

`verbo` |
Make this TRUE for detailed printing of computational steps |

`idep` |
The column number of the dependent variable (=1, default) |

This function calls `parcorHijk2`

function which
uses original data to compute
generalized partial correlations between `X_i`

, the dependent variable,
and `X_j`

which is the current regressor of interest. Note that
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 merges control variable(s) (if any) into `X_k`

.
Let the remainder effect
from OLS regressions of `X_i`

on `X_k`

equal the
residuals u(i,k). Analogously define u(j,k). It is a hybrid of OLS and generalized.
Finally, partial correlation is generalized (kernel) correlation
between u(i,k) and u(j,k).

A p by 1 ‘out’ vector containing hybrid partials r*(i,j | k).

Hybrid Generalized Partial Correlation Coefficients
(HGPCC) allow comparison of
the relative contribution of each `X_j`

to the explanation of `X_i`

,
because HGPCC are scale-free pure numbers.

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.

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

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 `parcor_ijk`

.

See Also `parcorVec`

.

```
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)
parcorVecH2(mtx)
## Not run:
set.seed(34);mtx=matrix(sample(1:600)[1:80],ncol=4)
colnames(mtx)=c('V1', 'v2', 'V3', 'V4')
parcorVecH2(mtx,verbo=TRUE, idep=2)
## End(Not run)
```

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