lmtestrob (version 0.1)

robfmtest: Robust Functional Specification Test

Description

Outlier robust test for functional miss-specification. It can be used to test linearity. The test is based on the robust Wald-type test by Heritier and Ronchetti (1994).

Usage

robfmtest(formula, power = 2:3, type = c("regressor"), data,
          x.weights = c("HAT", "MCD"), testtype = "Wald", ...)

Value

A list with class robfmtest containing the following components:

statistic

the value of the test statistic.

dof

the number of degrees of freedom.

method

a character string indicating what type of test was performed.

p.value

the p-value of the test.

data.name

a character string giving the name(s) of the data.

Arguments

formula

a symbolic description of the model to be tested.

power

integer(s). A vector of positive integers specifying the powers of the variables that should be tested. The default option tests second and third powers.

type

currently, only powers of regressors can be used.

data

an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which robfmtest is called.

x.weights

a string, indicating how the robustness weights on the covariates should be computed. The default option uses hat-matrix-based weights, second option allows to use robust Mahalanobis distance-based weights, where the Minimum Covariance Determinant is used to estimate location and scatter.

testtype

currently, the robust version of Wald test is implemented.

...

currently not used.

Author

Mikhail Zhelonkin

Details

Since the classical tests including resettest, raintest and harvtest implemented in lmtest are not resistant to outliers and can become misleading even in the presence of one outlier, we provide a test which is resistant to outliers. The price to pay for robustness is a small loss of power, when the model holds exactly.

References

Heritier, S., and Ronchetti, E. (1994) Robust Bounded-Influence Tests in General Parametric Models. Journal of the American Statistical Association, 89, p. 897-904.

Examples

set.seed(123)
n <- 50
x = runif(n, -3, 3)
y = rnorm(n)
example.dat <- data.frame(x, y)
robfmtest(y ~ x, data = example.dat)
library(lmtest)
resettest(y ~ x, data = example.dat, type = "fitted")
x[50] <- -3
y[50] <- -10
example.dat <- data.frame(x, y)
robfmtest(y ~ x, data = example.dat)
resettest(y ~ x, data = example.dat, type = "fitted")