silentMtx0: Older kernel-causality unanimity score matrix with optional...

View source: R/silentMtx0.R

silentMtx0R Documentation

Older kernel-causality unanimity score matrix with optional control variables


Allowing input matrix of control variables and missing data, this function produces a p by p matrix summarizing the results, where the estimated signs of stochastic dominance order values (+1, 0, –1) are weighted by wt=c(1.2, 1.1, 1.05, 1) to compute an overall result for all orders of stochastic dominance by a weighted sum for the criteria Cr1 and Cr2 and added to the Cr3 estimate as: (+1, 0, –1). Final weighted index is always in the range [–3.175, 3.175]. It is converted to the more intuitive range [–100, 100].


silentMtx0(mtx, ctrl = 0, dig = 6, wt = c(1.2, 1.1, 1.05, 1), sumwt = 4)



The data matrix with p columns. Denote x1 as the first column which is fixed and then paired with all other columns, say: x2, x3, .., xp, one by one for the purpose of flipping with x1. p must be 2 or more


data matrix for designated control variable(s) outside causal paths


Number of digits for reporting (default dig=6).


Allows user to choose a vector of four alternative weights for SD1 to SD4.


Sum of weights can be changed here =4(default).


The reason for slightly declining weights on the signs from SD1 to SD4 is simply that the local mean comparisons implicit in SD1 are known to be more reliable than local variance implicit in SD2, local skewness implicit in SD3 and local kurtosis implicit in SD4. Why are higher moment estimates less reliable? The higher power of the deviations from the mean needed in their computations lead to greater sampling variability. The summary results for all three criteria are reported in a vector of numbers internally called crall:


With p columns in mtx argument to this function, x1 can be paired with a total of p-1 columns (x2, x3, .., xp). Note we never flip any of the control variables with x1. This function produces i=1,2,..,p-1 numbers representing the summary sign, or ‘sum’ from the signs sg1 to sg3 associated with the three criteria: Cr1, Cr2 and Cr3. Note that sg1 and sg2 themselves are weighted signs using weighted sum of signs from four orders of stochastic dominance. In general, a positive sign in the i-th location of the ‘sum’ output of this function means that x1 is the kernel cause while the variable in (i+1)-th column of mtx is the ‘effect’ or ‘response’ or ‘endogenous.’ The magnitude represents the strength (unanimity) of the evidence for a particular sign. Conversely a negative sign in the i-th location of the ‘sum’ output of this function means that that the first variable listed as the input to this function is the ‘effect,’ while the variable in (i+1)-th column of mtx is the exogenous kernel cause. This function allows for control variables.


The European Crime data has all three criteria correctly suggesting that high crime rate kernel causes the deployment of a large number of police officers. The command attach(EuroCrime); silentPairs(cbind(crim,off)) returns only one number: 3.175, implying a high unanimity strength. The index 3.175 is the highest. The positive sign of the index suggests that ‘crim’ variable in the first column of the matrix input to this function kernel causes ‘off’ in the second column of the matrix argument mtx to this function.

Interpretation of the output matrix produced by this function is as follows. A negative index means the variable named in the column kernel-causes the variable named in the row. A positive index means the row name variable kernel-causes the column name variable. The abs(index) measures unanimity by three criteria, Cr1 to Cr3 representing the strength of evidence for the identified causal path.


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


H. D. Vinod '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("10.1080/03610918.2015.1122048")}

Vinod, H. D. Causal Paths and Exogeneity Tests in Generalcorr Package for Air Pollution and Monetary Policy (June 6, 2017). Available at SSRN:

See Also

See silentPairs0 using older Cr1 criterion based on kernel regression local gradients.

See someCPairs, some0Pairs


## Not run: 
silentMtx0(mtcars[,1:3],ctrl=mtcars[,4:5]) # mpg paired with others

## End(Not run)

## Not run: 
z=runif(10,2,11)# z is independently created
x=sample(1:10)+z/10 #x is somewhat indep and affected by z
silentMtx0(mtx=cbind(x2,y2), ctrl=cbind(z,w2))

## End(Not run)

generalCorr documentation built on Oct. 10, 2023, 1:06 a.m.