Estimating equation for multinomial logistic regression

Supports unranked categorical outcomes. y must be an n-by-k indicator matrix where the first column is the reference category, and k must be at least three: a two-level outcome is logistic regression, which ee_glm() fits with distribution = "binomial". Returns a (b * (k-1))-by-n matrix.

Usage

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

Arguments

theta

Numeric vector of length b * (k-1).

X

Numeric n-by-b design matrix.

y

Numeric n-by-k indicator matrix (first column = reference), with k at least three.

weights

Optional numeric vector of n weights. Default NULL.

offset

Optional numeric vector of n offsets. Default NULL.

Value

A (b * (k-1))-by-n matrix.

Examples

set.seed(123)
n <- 50
W <- rbinom(n, 1, 0.5)
probs <- cbind(0.5 - 0.2 * W, 0.3 + 0.1 * W, 0.2 + 0.1 * W)
y_cat <- sapply(seq_len(n), function(i) sample(1:3, 1, prob = probs[i, ]))

# The outcome is an indicator matrix whose first column is the reference
# category.
y <- cbind(
  as.integer(y_cat == 1),
  as.integer(y_cat == 2),
  as.integer(y_cat == 3)
)
X <- cbind(1, W)

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

# Two columns of X and two non-reference categories give four parameters.
m <- m_estimate(stacked_equations = psi, init = rep(0, 4))
coef(m)
#>   theta_1   theta_2   theta_3   theta_4 
#> -1.098612  1.386294 -1.098612  1.704748