In jrzubizarreta/depinf: Statistical Inference for Linear Unbiased Estimators under with Constrained Dependent Observations

Confidence intervals for linear unbiased estimators under constrained dependence

In this vignette, we replicate the main analyses in Section 5 of the paper.

########################
# Read packages

library("slam")
library("Rglpk")
library("gurobi")
library("sandwich")
library("lmtest")
library("depinf")

########################
# Load data

load("Russia_sathcap.Rsave")

########################
# Initialize basic variables

Y = cycle1$hiv
X = cycle1[,c("hcv","age","sex")]

n = length(Y)

# GR is the known elements of the adjacency matrix 

# find the recruitment degree of each subject
dr = apply(GR, 1, sum)

# if any total degree is less than the recruitment degree, correct it
cycle1$degree_corrected = pmax(cycle1$degree, dr)
d = cycle1$degree_corrected

########################
# Add an intercept 

X = as.matrix(cbind(1, X))

########################
# Calculate the Theta matrix 

Theta = solve(t(X)%*%X, t(X))

betahat = Theta %*% Y

########################
# Get the lm confidence intervals

linfit = lm(Y ~ hcv + age + sex, data = as.data.frame(X))

print(summary(linfit))

########################
# Get the naive and robust confidence intervals

# Naive
lmfit = lm(Y ~ X)
summary(lmfit)                                  

# Robust (Stata default)
coeftest(lmfit, vcov = vcovHC(lmfit, "HC1"))[, 2]

########################
# Build table

# Regression coefficients
col1 = betahat
# Naive standard errors
col2 = coef(summary(lmfit))[, 2]
# Robust standard errors
col3 = coeftest(lmfit, vcov = vcovHC(lmfit, "HC1"))[, 2]

dr = apply(GR, 1, sum)
cycle1$degree_corrected = pmax(cycle1$degree, dr)
d = cycle1$degree_corrected

# V1, no known dependencies (no GR)
a1 = sqrt(depvar(Y, Theta[1, ]*n, d, NULL, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
a2 = sqrt(depvar(Y, Theta[2, ]*n, d, NULL, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
a3 = sqrt(depvar(Y, Theta[3, ]*n, d, NULL, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
a4 = sqrt(depvar(Y, Theta[4, ]*n, d, NULL, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
col4 = c(a1, a2, a3, a4)

# V1, some known dependencies
b1 = sqrt(depvar(Y, Theta[1, ]*n, d, GR, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
b2 = sqrt(depvar(Y, Theta[2, ]*n, d, GR, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
b3 = sqrt(depvar(Y, Theta[3, ]*n, d, GR, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
b4 = sqrt(depvar(Y, Theta[4, ]*n, d, GR, case = "heteroskedastic", solver = "gurobi", approximate = 0)$V_hat)
col5 = c(b1, b2, b3, b4)

# V2, some known dependencies
c1 = sqrt(depvar(Y, Theta[1, ]*n, d, GR, case = "homoskedastic", solver = "gurobi", approximate = 0)$V_hat)
c2 = sqrt(depvar(Y, Theta[2, ]*n, d, GR, case = "homoskedastic", solver = "gurobi", approximate = 0)$V_hat)
c3 = sqrt(depvar(Y, Theta[3, ]*n, d, GR, case = "homoskedastic", solver = "gurobi", approximate = 0)$V_hat)
c4 = sqrt(depvar(Y, Theta[4, ]*n, d, GR, case = "homoskedastic", solver = "gurobi", approximate = 0)$V_hat)
col6 = c(c1, c2, c3, c4)

# V2'
d1 = sqrt(depvar(Y, Theta[1, ]*n, d, NULL, case = "homoskedastic")$V_hat)
d2 = sqrt(depvar(Y, Theta[2, ]*n, d, NULL, case = "homoskedastic")$V_hat)
d3 = sqrt(depvar(Y, Theta[3, ]*n, d, NULL, case = "homoskedastic")$V_hat)
d4 = sqrt(depvar(Y, Theta[4, ]*n, d, NULL, case = "homoskedastic")$V_hat)           
col7 = c(d1, d2, d3, d4)

tab = cbind(col1, col2, col3, col4, col5, col6, col7)
tab

########################
# Sensitivity analysis: solve for V1, V2 and V2' for d = cycle1$degree_corrected + k

for (j in 1:4) {

    #for (k in 0:(n-1)) {
    for (k in 0:2) {        

        cat("Coefficient ", j-1, ", iteration ", k, "\n", sep="")

        # V1
        out1 = depvar(y = Y, theta = Theta[j, ]*n, d = pmin(d+k, n-1), GR = GR, case = "heteroskedastic", solver = "gurobi", approximate = 1)

        # V2
        out2 = depvar(y = Y, theta = Theta[j, ]*n, d = pmin(d+k, n-1), GR = GR, case = "homoskedastic", solver = "gurobi", approximate = 1)

        # V2'
        x = Y*Theta[j, ]*n
        out3 = var(x)/n * (1 + sum(pmin(d+k, n-1))/n)

        aux1 = c(sqrt(out1$V_hat), betahat[j]-1.96*sqrt(out1$V_hat), betahat[j]+1.96*sqrt(out1$V_hat))
        aux2 = c(sqrt(out2$V_hat), betahat[j]-1.96*sqrt(out2$V_hat), betahat[j]+1.96*sqrt(out2$V_hat))
        aux3 = c(sqrt(out3), betahat[j]-1.96*sqrt(out3), betahat[j]+1.96*sqrt(out3)) 

        temp = rbind(aux1, aux2, aux3)
        rownames(temp) = c(paste("V1, k =", k, sep = " "), paste("V2, k =", k, sep = " "), paste("V2', k =", k, sep = " "))
        colnames(temp) = c("s.e", "(", ")")

        if (k == 0) {
            tab = temp
        }
        else {
            tab = rbind(tab, temp)
        }
    }
    assign(paste('tab_beta', j-1, sep=''), tab)
}

tab_approx = tab

sink("tab_approx.txt")

cat("Intercept", "\n")
tab_beta0

cat("\n", "Beta 1", "\n")
tab_beta1

cat("\n", "Beta 2", "\n")
tab_beta2

cat("\n", "Beta 3", "\n")
tab_beta3

save(tab_beta0, tab_beta1, tab_beta2, tab_beta3, file = "tab_approx.RData")

jrzubizarreta/depinf documentation built on May 20, 2019, 2:07 a.m.