Package 'RcppNumerical'

Fast Logistic Regression Fitting Using L-BFGS Algorithm

Description

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.

Usage

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 $|f-f'|/|f|<\epsilon_f$, where $f$ and $f'$ are the current and previous value of the objective function (negative log likelihood) respectively.
eps_g	Iteration stops if $||g|| < \epsilon_g * \max(1, ||\beta||)$, where $\beta$ is the current coefficient vector and $g$ is the gradient.
maxit	Maximum number of iterations.

Value

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., $X\hat{\beta}$
loglikelihood	The maximized log likelihood
converged	Whether the optimization algorithm has converged

Author(s)

Yixuan Qiu https://statr.me

See Also

glm.fit()

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))

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