FitBNR function

Fit Bivariate Normal Regression Model

Estimation procedure for bivariate normal regression models. The EM algorithm is applied if s contains missing values, or if X differs from Z. Otherwise, an accelerated least squares procedure is applied.

FitBNR(t, s, X, Z = NULL, sig = 0.05, ...)

Arguments

• t: Target outcome vector.
• s: Surrogate outcome vector.
• X: Target model matrix.
• Z: Surrogate model matrix. Defaults to X.
• sig: Significance level.
• ...: Additional arguments accepted if fitting via EM. See FitBNEM.

Returns

An object of class 'mnr' with slots containing the estimated regression coefficients, the target-surrogate covariance matrix, the information matrices for regression parameters, and the residuals.

Details

The target and surrogate model matrices are expected in numeric format. Include an intercept if required. Expand factors and interactions in advance.

Examples

# Case 1: No surrogate missingness.
set.seed(100)
n <- 1e3
X <- stats::rnorm(n)
data <- rBNR(
  X = X,
  Z = X,
  b = 1,
  a = -1,
  t_miss = 0.1,
  s_miss = 0.0
)
t <- data[, 1]
s <- data[, 2]

# Model fit.
fit_bnls <- FitBNR(
  t = t,
  s = s,
  X = X
)

# Case 2: Target and surrogate missingness.
set.seed(100)
n <- 1e3
X <- stats::rnorm(n)
Z <- stats::rnorm(n)
data <- rBNR(
  X = X,
  Z = Z,
  b = 1,
  a = -1,
  t_miss = 0.1,
  s_miss = 0.1
)

# Log likelihood.
fit_bnem <- FitBNR(
  t = data[, 1],
  s = data[, 2],
  X = X,
  Z = Z
)