fastLR function

Fast Logistic Regression Fitting Using L-BFGS Algorithm

fastLR() uses the L-BFGS algorithm to efficiently fit logistic regression. It is in fact an application of the C++ function optim_lbfgs() provided by RcppNumerical to perform L-BFGS optimization.

fastLR(
  x,
  y,
  start = rep(0, ncol(x)),
  eps_f = 1e-08,
  eps_g = 1e-05,
  maxit = 300
)

Arguments

• x: The model matrix.
• y: The response vector.
• start: The initial guess of the coefficient vector.
• eps_f: Iteration stops if $|f-f'|/|f|<eps_f$, where $f$ and $f'$ are the current and previous value of the objective function (negative log likelihood) respectively.
• eps_g: Iteration stops if $||g|| < eps_g * max(1, ||beta||)$, where $beta$ is the current coefficient vector and $g$ is the gradient.
• maxit: Maximum number of iterations.

Returns

fastLR() returns a list with the following components: - coefficients: Coefficient vector

• fitted.values: The fitted probability values

• linear.predictors: The fitted values of the linear part, i.e., $X * beta_hat$

• loglikelihood: The maximized log likelihood

• converged: Whether the optimization algorithm has converged

Examples

set.seed(123)
n = 1000
p = 100
x = matrix(rnorm(n * p), n)
beta = runif(p)
xb = c(x %*% beta)
p = 1 / (1 + exp(-xb))
y = rbinom(n, 1, p)

system.time(res1 <- glm.fit(x, y, family = binomial()))
system.time(res2 <- fastLR(x, y))
max(abs(res1$coefficients - res2$coefficients))

See Also

glm.fit()

Author(s)

Yixuan Qiu https://statr.me