R: Harvey-Collier Test

harvtest {lmtest} | R Documentation

## Harvey-Collier Test

### Description

Harvey-Collier test for linearity.

### Usage

    harvtest(formula, order.by = NULL, data = list())

### Arguments

`formula` | a symbolic description for the model to be tested (or a fitted `"lm"` object).
`order.by` | Either a vector `z` or a formula with a single explanatory variable like `~ z`. The observations in the model are ordered by the size of `z`. If set to `NULL` (the default) the observations are assumed to be ordered (e.g., a time series).
`data` | an optional data frame containing the variables in the model. By default the variables are taken from the environment which `harvtest` is called from.

### Details

The Harvey-Collier test performs a t-test (with `parameter` degrees of freedom) on the recursive residuals. If the true relationship is not linear but convex or concave the mean of the recursive residuals should differ from 0 significantly.

Examples can not only be found on this page, but also on the help pages of the data sets `bondyield`, `currencysubstitution`, `growthofmoney`, `moneydemand`, `unemployment`, `wages`.

### Value

A list with class `"htest"` containing the following components:

`statistic` | the value of the test statistic.
`p.value` | the p-value of the test.
`parameter` | degrees of freedom.
`method` | a character string indicating what type of test was performed.
`data.name` | a character string giving the name(s) of the data.

### References

A. Harvey & P. Collier (1977), Testing for Functional Misspecification in Regression Analysis. Journal of Econometrics 6, 103–119

W. Krämer & H. Sonnberger (1986), The Linear Regression Model under Test. Heidelberg: Physica

### See Also

`lm`

### Examples

    # generate a regressor and dependent variable
    x <- 1:50
    y1 <- 1 + x + rnorm(50)
    y2 <- y1 + 0.3*x^2

    ## perform Harvey-Collier test
    harv <- harvtest(y1 ~ x)
    harv
    ## calculate critical value vor 0.05 level
    qt(0.95, harv$parameter)
    harvtest(y2 ~ x)

[Package lmtest version 0.9-37 Index]