Regression Calibration for Measurement Error Correction

Source: R/rcreg.R

rcreg is used to correct a regression object with a continuous independent variable measured with error via regression calibration by Carroll et al. (1995).

rcreg(
  reg = NULL,
  formula = NULL,
  data = NULL,
  weights = NULL,
  MEvariable = NULL,
  MEerror = NULL,
  variance = FALSE,
  nboot = 400
)

# S3 method for rcreg
coef(object, ...)

# S3 method for rcreg
vcov(object, ...)

# S3 method for rcreg
sigma(object, ...)

# S3 method for rcreg
formula(x, ...)

# S3 method for rcreg
family(object, ...)

# S3 method for rcreg
predict(object, ...)

# S3 method for rcreg
model.frame(formula, ...)

# S3 method for rcreg
print(x, ...)

# S3 method for rcreg
summary(object, ...)

# S3 method for summary.rcreg
print(x, digits = 4, ...)

# S3 method for rcreg
update(object, ..., evaluate = TRUE)

Arguments

reg

naive regression object. See Details.
formula

regression formula
data

new dataset for reg
weights

new weights for reg
MEvariable

variable measured with error
MEerror

standard deviation of the measurement error
variance

a logical value. If TRUE, correct the var-cov matrix of coefficients by bootstrapping. Default is FALSE.
nboot

number of boots for correcting the var-cov matrix of coefficients. Default is 400.
object

an object of class rcreg
...

additional arguments
x

an object of class rcreg
digits

minimal number of significant digits. See print.default.
evaluate

a logical value. If TRUE, the updated call is evaluated. Default is TRUE.

Value

If MEvariable is not in the regression formula, reg is returned. If MEvariable is a continuous independent variable in the regression formula, an object of class rcreg is returned:

call

the function call,

NAIVEreg

the naive regression object,

ME

a list of MEvariable, MEerror, variance and nboot,

RCcoef

coefficient estimates corrected by regression calibration,

RCsigma

the residual standard deviation of a linear regression object corrected by regression calibration,

RCvcov

the var-cov matrix of coefficients corrected by regression calibration,

...

Details

reg fitted by lm, glm (with family gaussian, binomial or poisson), multinom, polr, coxph or survreg is supported.

Methods (by generic)

  • coef: Extract coefficients corrected by rcreg

  • vcov: Extract the var-cov matrix of coefficients corrected by rcreg

  • sigma: Extract the residual standard deviation of a linear regression object corrected by rcreg

  • formula: Extract the regression formula

  • family: Extract the family of a regression of class lm or glm

  • predict: Predict with new data

  • model.frame: Extract the model frame

  • print: Print results of rcreg nicely

  • summary: Summarize results of rcreg nicely

  • print: Print summary of rcreg nicely

  • update: Update rcreg

References

Carrol RJ, Ruppert D, Stefanski LA, Crainiceanu C (2006). Measurement Error in Nonlinear Models: A Modern Perspective, Second Edition. London: Chapman & Hall.

See also

simexreg, cmsens, cmest

Examples


if (FALSE) {
rm(list=ls())
library(CMAverse)

# 2 boots are used for illustration
# lm
n <- 1000
x1 <- rnorm(n, mean = 5, sd = 3)
x2_true <- rnorm(n, mean = 2, sd = 1)
error1 <- rnorm(n, mean = 0, sd = 0.5)
x2_error <- x2_true + error1
x3 <- rbinom(n, size = 1, prob = 0.4)
y <- 1 + 2 * x1 + 4 * x2_true + 2 * x3  + rnorm(n, mean = 0, sd = 2)
data <- data.frame(x1 = x1, x2_true = x2_true, x2_error = x2_error,
                   x3 = x3, y = y)
reg_naive <- lm(y ~ x1 + x2_error + x3, data = data)
reg_true <- lm(y ~ x1 + x2_true + x3, data = data)
reg_rc <- rcreg(reg = reg_naive, data = data, MEvariable = "x2_error", MEerror = 0.5, 
variance = TRUE, nboot = 2)
coef(reg_rc)
vcov(reg_rc)
sigma(reg_rc)
formula(reg_rc)
family(reg_rc)
predict(reg_rc, newdata = data[1, ])
reg_rc_model <- model.frame(reg_rc)
reg_rc_update <- update(reg_rc, data = data, weights = rep(1, n))
reg_rc_summ <- summary(reg_rc)

#glm
n <- 1000
x1 <- rnorm(n, mean = 0, sd = 1)
x2_true <- rnorm(n, mean = 1, sd = 1)
error1 <- rnorm(n, mean = 0, sd = 0.5)
x2_error <- x2_true + error1
x3 <- rbinom(n, size = 1, prob = 0.4)
linearpred <- 1 + 0.3 * x1 - 0.5 * x2_true - 0.2 * x3
py <- exp(linearpred) / (1 + exp(linearpred))
y <- rbinom(n, size = 1, prob = py)
data <- data.frame(x1 = x1, x2_true = x2_true, x2_error = x2_error,
                   x3 = x3, y = y)
reg_naive <- glm(y ~ x1 + x2_error + x3, data = data, family = binomial("logit"))
reg_true <- glm(y ~ x1 + x2_true + x3, data = data, family = binomial("logit"))
reg_rc <- rcreg(reg = reg_naive, data = data, 
MEvariable = "x2_error", MEerror = 0.5, variance = TRUE, nboot = 2)

# multinom
n <- 1000
x1 <- rnorm(n, mean = 0, sd = 1)
x2_true <- rnorm(n, mean = 1, sd = 1)
error1 <- rnorm(n, mean = 0, sd = 0.5)
x2_error <- x2_true + error1
x3 <- rbinom(n, size = 1, prob = 0.4)
linearpred1 <- 1 + 0.3 * x1 - 0.5 * x2_true - 0.2 * x3
linearpred2 <- 2 + 1 * x1 - 2 * x2_true - 1 * x3
py2 <- exp(linearpred1) / (1 + exp(linearpred1) + exp(linearpred2))
py3 <- exp(linearpred2) / (1 + exp(linearpred1) + exp(linearpred2))
py1 <- 1 - py2 - py3
y <- sapply(1:n, function(x) sample(size = 1, c(1:3), prob = c(py1[x], py2[x], py3[x])))
data <- data.frame(x1 = x1, x2_true = x2_true, x2_error = x2_error,
                   x3 = x3, y = y)
reg_naive <- nnet::multinom(factor(y) ~ x1 + x2_error + x3, data = data)
reg_true <- nnet::multinom(factor(y) ~ x1 + x2_true + x3, data = data)
reg_rc <- rcreg(reg = reg_naive, data = data, MEvariable = "x2_error", MEerror = 0.5, 
variance = TRUE, nboot = 2)
}