lm.mle: 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,
  ...
)

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".

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.

Examples

Run this code


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)