Regression Calibration for Measurement Error Correction

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,

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(rcreg): Extract coefficients corrected by rcreg
vcov(rcreg): Extract the var-cov matrix of coefficients corrected by rcreg
sigma(rcreg): Extract the residual standard deviation of a linear regression object corrected by rcreg
formula(rcreg): Extract the regression formula
family(rcreg): Extract the family of a regression of class lm or glm
predict(rcreg): Predict with new data
model.frame(rcreg): Extract the model frame
print(rcreg): Print results of rcreg nicely
summary(rcreg): Summarize results of rcreg nicely
update(rcreg): Update rcreg

Functions

print(summary.rcreg): Print summary of rcreg nicely

References

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

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)
}