tls {tls}

Fitting error-in-variables models via total least squares.

Description

It can be used to carry out regression models that account for measurement errors in the independent variables.

Usage

tls(formula, data, method = c("normal", "bootstrap"), conf.level = 0.95,
  ...)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.

method

method for computing confidence interval

conf.level

the confidence level for confidence interval.

...

Optional arguments for future usage.

Details

This function should be used with care. Confidence interval estimation is given by normal approximation or bootstrap. The normal approximation and bootstrap are proper when all the error terms are independent from normal distribution with zero mean and equal variance (see the references for more details).

Value

tls returns parameters of the fitted model including estimations of coefficient, corresponding estimated standard errors and confidence intervals.

Author(s)

Yan Li

References

• Gleser, Estimation in a Multivariate "Errors in Variables" Regression Model: Large Sample Results, 1981, Ann. Stat.

• Golub and Laon, An Analysis of the Total Least Squares Problem, 1980, SIAM J. Numer. Anal.

• Pesta, Total least squares and bootstrapping with applications in calibration, 2012, Statistics.

Examples

library(tls)
set.seed(100)
X.1 <- sqrt(1:100)
X.tilde.1 <- rnorm(100) + X.1
X.2 <- sample(X.1, size = length(X.1), replace = FALSE)
X.tilde.2 <- rnorm(100) + X.2
Y <- rnorm(100) + X.1 + X.2
data <- data.frame(Y = Y, X.1 = X.tilde.1, X.2 = X.tilde.2)
tls(Y ~ X.1 + X.2 - 1, data = data)