causeAllPair function

All Pair Version Kernel (block) causality summary paths from three criteria

Allowing input matrix of control variables, this function produces a 5 column 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). The final range for the unanimity of sign index is [--100, 100].

causeAllPair(
  mtx,
  nam = colnames(mtx),
  blksiz = 10,
  ctrl = 0,
  dig = 6,
  wt = c(1.2, 1.1, 1.05, 1),
  sumwt = 4
)

Arguments

• mtx: The data matrix with many columns, We consider causal paths among all possible pairs of mtx columns.
• nam: vector of column names for mtx. Default: colnames(mtx)
• blksiz: block size, default=10, if chosen blksiz >n, where n=rows in matrix then blksiz=n. That is, no blocking is done
• ctrl: data matrix for designated control variable(s) outside causal paths
• dig: Number of digits for reporting (default dig=6).
• wt: Allows user to choose a vector of four alternative weights for SD1 to SD4.
• sumwt: Sum of weights can be changed here =4(default).

Returns

If there are p columns in the input matrix, x1, x2, .., xp, say, there are choose(p,2) or [p*(p-1)/2] possible pairs and as many causal paths. This function returns a matrix of p*(p-1)/2 rows and 5 columns entitled: cause", response", strength", corr." and ``p-value", respectively with self-explanatory titles. The first two columns have names of variables x1 or x(1+j), depending on which is the cause. The strength' column has absolute value of summary index in range [0,100] providing summary of causal results based on preponderance of evidence from criteria Cr1 to Cr3 from four orders of stochastic dominance, etc. The fourth column corr.' reports the Pearson correlation coefficient while the fifth column has the p-value for testing the null of zero Pearson coeff. This function merely calls causeSumNoP repeatedly to include all pairs. The background function siPairsBlk allows for control variables. The output of this function can be sent to `xtable' for a nice Latex table.

Details

The reason for slightly declining weights on the signs from SD1 to SD4 stochastic dominance orders is simply their slightly increasing sampling unreliability due to higher order trapezoidal approximations of integrals of densities involved in definitions of SD1 to SD4. The summary results for all three criteria are reported in one matrix called out:

Note

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. Since Cr1 to Cr3 near unanimously suggest crim' as the cause of off', strength index 100 suggests unanimity. attach(EuroCrime); causeSummary(cbind(crim,off))

Examples

## Not run:

mtx=data.frame(mtcars[,1:3]) #make sure columns of mtx have names
ctrl=data.frame(mtcars[,4:5])
 causeAllPair(mtx=mtx,ctrl=ctrl)
## End(Not run)

options(np.messages=FALSE)
set.seed(234)
z=runif(10,2,11)# z is independently created
x=sample(1:10)+z/10 #x is somewhat indep and affected by z
y=1+2*x+3*z+rnorm(10)
w=runif(10)
x2=x;x2[4]=NA;y2=y;y2[8]=NA;w2=w;w2[4]=NA
causeAllPair(mtx=cbind(x2,y2), ctrl=cbind(z,w2))

References

Vinod, H. D. `Generalized Correlation and Kernel Causality with Applications in Development Economics' in Communications in Statistics -Simulation and Computation, 2015, tools:::Rd_expr_doi("10.1080/03610918.2015.1122048")

Vinod, H. D. 'New exogeneity tests and causal paths,' Chapter 2 in 'Handbook of Statistics: Conceptual Econometrics Using R', Vol.32, co-editors: H. D. Vinod and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2019, pp. 33-64.

Vinod, H. D. Causal Paths and Exogeneity Tests in Generalcorr Package for Air Pollution and Monetary Policy (June 6, 2017). Available at SSRN: https://www.ssrn.com/abstract=2982128

See Also

See bootPairs, causeSummBlk

See someCPairs

siPairsBlk, causeSummary

Author(s)

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