one_step: One-step maximum likelihood estimation

In MLBC: Bias Correction Methods for Models Using Synthetic Data

One-step maximum likelihood estimation

Description

Maximum likelihood estimation of the regression model, treating the generated covariate as a noisy proxy for the true latent variable. This method is particularly useful when an estimate of the false positive rate is not available. The variance of the estimates is approximated via the inverse Hessian at the optimum.

Usage

one_step(
  Y,
  Xhat = NULL,
  homoskedastic = FALSE,
  distribution = c("normal", "t", "laplace", "gamma", "beta"),
  nu = 4,
  gshape = 2,
  gscale = 1,
  ba = 2,
  bb = 2,
  intercept = TRUE,
  gen_idx = 1,
  data = parent.frame(),
  ...
)

## Default S3 method:
one_step(
  Y,
  Xhat,
  homoskedastic = FALSE,
  distribution = c("normal", "t", "laplace", "gamma", "beta"),
  nu = 4,
  gshape = 2,
  gscale = 1,
  ba = 2,
  bb = 2,
  intercept = TRUE,
  gen_idx = 1,
  ...
)

## S3 method for class 'formula'
one_step(
  Y,
  Xhat = NULL,
  homoskedastic = FALSE,
  distribution = c("normal", "t", "laplace", "gamma", "beta"),
  nu = 4,
  gshape = 2,
  gscale = 1,
  ba = 2,
  bb = 2,
  intercept = TRUE,
  gen_idx = 1,
  data = parent.frame(),
  ...
)

Arguments

Y	numeric response vector, or a one-sided formula
Xhat	numeric matrix of regressors (if Y is numeric)
homoskedastic	logical; if TRUE, assumes a common error variance; otherwise, the error variance is allowed to vary with the true latent binary variable
distribution	character; distribution for error terms. One of "normal", "t", "laplace", "gamma", "beta"
nu	numeric; degrees of freedom (for Student-t distribution)
gshape	numeric; shape parameter (for Gamma distribution)
gscale	numeric; scale parameter (for Gamma distribution)
ba	numeric; alpha parameter (for Beta distribution)
bb	numeric; beta parameter (for Beta distribution)
intercept	logical; if TRUE, prepend an intercept column to Xhat
gen_idx	integer; index (1-based) of the binary ML-generated variable. If not specified, defaults to the first non-intercept variable
data	data frame (if Y is a formula)
...	unused

Value

An object of class mlbc_fit and mlbc_onestep with:

• coef: estimated regression coefficients

• vcov: variance-covariance matrix

Usage Options

Option 1: Formula Interface

• Y: A one-sided formula string

• data: Data frame containing the variables referenced in the formula

Option 2: Array Interface

• Y: Response variable vector

• Xhat: Design matrix of covariates

Examples

# Load the remote work dataset
data(SD_data)

# Basic one-step estimation
fit_onestep <- one_step(log(salary) ~ wfh_wham + soc_2021_2 + employment_type_name,
                        data = SD_data)
summary(fit_onestep)

# With different error distribution
fit_t <- one_step(log(salary) ~ wfh_wham + soc_2021_2,
                  data = SD_data,
                  distribution = "t",
                  nu = 4)
summary(fit_t)

# Homoskedastic errors
fit_homo <- one_step(log(salary) ~ wfh_wham + soc_2021_2,
                     data = SD_data,
                     homoskedastic = TRUE)
summary(fit_homo)

MLBC documentation built on Aug. 8, 2025, 7:31 p.m.