Fit a model via maximum likelihood

Finds the maximum likelihood estimates of parameters and returns a fitted model object with standard errors, confidence intervals, and other inference quantities computed automatically via autodiff.

Usage

fit(
  loglik,
  params,
  method = c("bfgs", "lbfgs", "newton", "gradient"),
  predict_fn = NULL,
  ...
)

Arguments

loglik

A log-likelihood function. Can be specified in two ways:

• Named arguments: function(mu, sigma) loglik_normal(mu, sigma, x)

• Single parameter argument: function(p) loglik_normal(p$mu, p$sigma, x)

The function should return a scalar value object.

params

Named numeric vector of initial parameter values, e.g., c(mu = 0, sigma = 1).

method

Optimization method: "bfgs" (default), "lbfgs", "newton", or "gradient".

predict_fn

Optional prediction function. Should take arguments (params, newdata) where params is a named list of parameter values and newdata is the new data for prediction. If provided, enables use of predict() on the fitted model.

...

Additional arguments passed to the optimizer.

Value

A femtofit object containing:

• Coefficient estimates (accessible via coef())

• Variance-covariance matrix (accessible via vcov())

• Log-likelihood value (accessible via logLik())

• Standard errors, Hessian, convergence info

Examples

if (FALSE) { # \dontrun{
# Generate data
set.seed(42)
x <- rnorm(100, mean = 5, sd = 2)

# Fit using named arguments (recommended)
result <- fit(
  function(mu, sigma) loglik_normal(mu, sigma, x),
  params = c(mu = 0, sigma = 1)
)

# Or using single parameter argument
result <- fit(
  function(p) loglik_normal(p$mu, p$sigma, x),
  params = c(mu = 0, sigma = 1)
)

# Standard R generics work
coef(result)      # Parameter estimates
vcov(result)      # Variance-covariance matrix
confint(result)   # 95% confidence intervals
logLik(result)    # Log-likelihood (works with AIC/BIC)
AIC(result)       # Akaike information criterion
summary(result)   # Full summary with p-values
} # }