A simulation to look at how distance based correlation can work with D-sep tests

conditional_independence_dcov.R

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#' @title  Fisher's C and Distance Correlation
#' 
#' @author Jarrett Byrnes
#' 
#' @description A simulation to look at 
#' how distance based correlation can work with 
#' D-sep tests
#' 
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#for data manipulation
library(dplyr)

#install.packages("energy") #for dcor
library(energy) 

#sample size
n <- 100

#Make a data frame with two nonlinear relationships
test_data_frame <- data.frame(a = runif(n,20,40)) %>%
  mutate(b = rnorm(n, 2*a, 5),
         c = rgamma(n, rate = 10/exp(0.2*a), shape=10),
         d = rgamma(n, rate=1/exp(0.01*b-0.005*c), shape=1))

#visualize
pairs(test_data_frame)

#The model
mod1 <- lm(b ~ a, data=test_data_frame)
mod2 <- glm(c ~ a, family=Gamma(link="log"), data=test_data_frame)
mod3 <- glm(d ~ b + c, family=Gamma(link="log"), data=test_data_frame)

#look at results
summary(mod1)
summary(mod2)
summary(mod3)

#classic basis set test
test1_classic <- lm(b ~ a + c, data=test_data_frame)
test1a_classic <- glm(c ~ a + b, family=Gamma(link="log"), data=test_data_frame)
test2_classic <- glm(d ~ b + c + a, family=Gamma(link="log"), data=test_data_frame)

#testing the basis set with distance based covariance
test1 <- dcov.test(residuals(mod1),test_data_frame$c)
test1a <- dcov.test(residuals(mod2), test_data_frame$b)
test2 <- dcov.test(residuals(mod3), test_data_frame$a)


#compare at the results
coef(summary(test1_classic))
coef(summary(test1a_classic))

test1
test1a

##########################

#Fisher's C
fishers_c <- -2*(log(test1$p.value) + log(test2$p.value))
fishers_c

#The test
pchisq(fishers_c, 4)