Estimating equation for beta regression

Beta regression for outcomes in (0, 1) using mean-precision parameterization. The last element of theta is log(phi), the log precision parameter.

Usage

ee_beta_regression(theta, X, y, weights = NULL, offset = NULL)

Arguments

theta

Numeric vector of length b + 1.

X

Numeric n-by-b design matrix.

y

Numeric vector of n outcomes in (0, 1).

weights

Optional numeric vector of n weights. Default NULL.

offset

Optional numeric vector of n offsets. Default NULL.

Value

A (b+1)-by-n matrix. The rows are named X_1 through X_b for the columns of X, and the final row is named log_phi.

Examples

set.seed(42)
n <- 50
W <- rnorm(n)
mu <- 1 / (1 + exp(-(0.5 + 0.3 * W)))
y <- rbeta(n, shape1 = mu * 10, shape2 = (1 - mu) * 10)
X <- cbind(1, W)

psi <- function(theta) ee_beta_regression(theta, X = X, y = y)

# The last parameter is log(phi), started here at a precision of 10. The
# default solver diverges on this equation, so use nleqslv.
m <- m_estimate(
  stacked_equations = psi,
  init = c(0, 0, log(10)),
  solver = "nleqslv"
)
coef(m)
#>       X_1       X_2   log_phi 
#> 0.4620901 0.2783017 2.5566274