lm.mle: Linear Regression via MLE

In snreg: Regression with Skew-Normally Distributed Error Term

Linear Regression via MLE

Description

lm.mle fits a linear regression model by maximum likelihood, allowing for optional multiplicative heteroskedasticity in the disturbance variance via a log-linear specification provided through ln.var.v.

Usage

lm.mle(
  formula,
  data,
  subset,
  ln.var.v = NULL,
  technique = c("bfgs"),
  lmtol = 1e-05,
  reltol = 1e-12,
  maxit = 199,
  optim.report = 1,
  optim.trace = 10,
  print.level = 0,
  digits = 4,
  only.data = FALSE,
  ...
)

Arguments

formula	an object of class formula specifying the regression: typically y ~ x1 + ..., where y is the dependent variable and the x's are regressors.
data	an optional data.frame containing the variables referenced in formula. If not found in data, variables are taken from environment(formula).
subset	an optional logical or numeric vector specifying the subset of observations to be used in estimation.
ln.var.v	optional one-sided formula; e.g. ln.var.v ~ z1 + z2. When provided, the error variance is modeled as \log(\sigma_i^2) = w_i^\top \gamma_v. If NULL, the variance is homoskedastic.
technique	character vector specifying the preferred optimization routine(s) in order of preference. Recognized keywords (for future implementation) include "bfgs" "bhhh", "nm" (Nelder–Mead), "bfgs", and "cg". Default is "bfgs". This scaffold records but does not execute the chosen routine.
lmtol	numeric. Convergence tolerance based on scaled gradient (when applicable). Default 1e-5.
reltol	numeric. Relative convergence tolerance for likelihood maximization. Default 1e-12.
maxit	integer. Maximum number of iterations for the optimizer. Default 199.
optim.report	integer. Verbosity level for reporting progress (if implemented). Default 1.
optim.trace	integer. Trace level for optimization (if implemented). Default 1.
print.level	integer. Printing level for summaries. Default 0.
digits	integer. Number of digits for printing. Default 4.
only.data	logical. If TRUE, returns only constructed data/matrices without estimation. Default FALSE.
...	additional arguments reserved for future methods (e.g., bounds, penalties).

Details

Linear Model by Maximum Likelihood (with optional heteroskedasticity)

This function fits a maximum-likelihood linear model.

The model is

y_i = x_i^\top \beta + \varepsilon_i,\quad \varepsilon_i \sim \mathcal{N}(0, \sigma_i^2).

When ln.var.v is supplied, the variance follows

\log(\sigma_i^2) = w_i^\top \gamma_v,

otherwise \sigma_i^2 = \sigma^2 is constant (homoskedastic).

This function:

• Builds the model frame and X, y.

• Builds Zv for the log-variance index when ln.var.v is provided.

• Returns a structured object with placeholders for coef, vcov, loglik.

Insert your MLE engine to estimate \beta, and (optionally) \sigma^2 or \gamma_v; compute standard errors via AIM/OPG as required by vcetype.

Value

A list of class "snreg" containing:

par	Numeric vector of MLE parameter estimates.
value	Maximized log-likelihood.
ll	Maximized log-likelihood (alias).
counts	Number of function evaluations (from optim).
convergence	Convergence code from optim.
message	Message returned by optim.
hessian	Observed Hessian matrix at optimum.
coef	Named coefficient vector; equal to par.
vcov	Variance–covariance matrix solve(-hessian).
sds	Standard errors: sqrt(diag(vcov)).
ctab	Coefficient table with columns: Estimate, Std.Err, Z value, Pr(>z).
esample	Logical vector: observations used in estimation.
n	Number of observations in estimation sample.

The object inherits the default optim components and is assigned class "snreg".

See Also

snsf, snreg

Examples

library(snreg)

data("banks07")
head(banks07)

# Translog cost function specification

spe.tl <- log(TC) ~ (log(Y1) + log(Y2) + log(W1) + log(W2))^2 +
  I(0.5 * log(Y1)^2) + I(0.5 * log(Y2)^2) +
  I(0.5 * log(W1)^2) + I(0.5 * log(W2)^2)

# Specification 1: homoskedastic noise (ln.var.v = NULL)

formSV <- NULL   # variance equation; constant variance

m1 <- lm.mle(
  formula   = spe.tl,
  data      = banks07,
  ln.var.v  = formSV
)

summary(m1)

# Specification 2: heteroskedastic

formSV <- ~ log(TA)      # variance equation; heteroskedastic noise (variance depends on TA)

m2 <- lm.mle(
  formula   = spe.tl,
  data      = banks07,
  ln.var.v  = formSV
)

summary(m2)

snreg documentation built on Feb. 6, 2026, 5:08 p.m.