man/examples/new_methods.R

In cirls: Constrained Iteratively Reweighted Least Squares

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# Isotonic regression

#----- Perform isotonic regression

# Generate data
set.seed(222)
p1 <- 5; p2 <- 3
x1 <- matrix(rnorm(100 * p1), 100, p1)
x2 <- matrix(rnorm(100 * p2), 100, p2)
b1 <- runif(p1) |> sort()
b2 <- runif(p2)
y <- x1 %*% b1 + x2 %*% b2 + rnorm(100, sd = 2)

# Fit model
Ciso <- diff(diag(p1))
resiso <- glm(y ~ x1 + x2, method = cirls.fit, Cmat = list(x1 = Ciso))

#----- Extract uncertainty

# Extract variance covariance
vcov(resiso)

# Extract confidence intervals
confint(resiso)

# We can extract the usual unconstrained matrix
vcov(resiso, constrained = FALSE)
all.equal(vcov(resiso, constrained = FALSE), summary(resiso)$cov.scaled)

# Simulate from the distribution of coefficients
sims <- simulCoef(resiso, nsim = 10)

# Check that all simulated coefficient vectors are feasible
apply(resiso$Cmat %*% t(sims) >= resiso$lb, 2, all)