Goldfeld–Quandt test

In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses.wikipedia
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Homoscedasticity

homoscedastichomogeneity of variancehomoskedastic
In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses.
Testing for groupwise heteroscedasticity requires the Goldfeld–Quandt test.

Stephen Goldfeld

Stephen M. GoldfeldGoldfeld, Stephen M.
The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt.

Richard E. Quandt

Richard Quandt
The Goldfeld–Quandt test is one of two tests proposed in a 1965 paper by Stephen Goldfeld and Richard Quandt.
* Goldfeld–Quandt test

F-test of equality of variances

F testF''-testFisher's F
This test statistic corresponds to an F-test of equality of variances, and a one- or two-sided test may be appropriate depending on whether or not the direction of the supposed relation of the error variance to the explanatory variable is known.

Statistics

statisticalstatistical analysisstatistician
In statistics, the Goldfeld–Quandt test checks for homoscedasticity in regression analyses.

Regression analysis

regressionmultiple regressionregression model
In the context of multiple regression (or univariate regression), the hypothesis to be tested is that the variances of the errors of the regression model are not constant, but instead are monotonically related to a pre-identified explanatory variable.

Dependent and independent variables

dependent variableindependent variableexplanatory variable
In the context of multiple regression (or univariate regression), the hypothesis to be tested is that the variances of the errors of the regression model are not constant, but instead are monotonically related to a pre-identified explanatory variable.

Least squares

least-squaresmethod of least squaresleast squares method
The parametric test is accomplished by undertaking separate least squares analyses on two subsets of the original dataset: these subsets are specified so that the observations for which the pre-identified explanatory variable takes the lowest values are in one subset, with higher values in the other.

Parametric statistics

parametricparametric testparametric inference
The parametric test assumes that the errors have a normal distribution.

Normal distribution

normally distributedGaussian distributionnormal
The parametric test assumes that the errors have a normal distribution. The second test proposed in the paper is a nonparametric one and hence does not rely on the assumption that the errors have a normal distribution.

Design matrix

data matrixdesign matricesdata matrices
There is an additional assumption here, that the design matrices for the two subsets of data are both of full rank.

Test statistic

Common test statisticst''-test of test statistics
The test statistic used is the ratio of the mean square residual errors for the regressions on the two subsets.

Power (statistics)

statistical powerpowerpowerful
Increasing the number of observations dropped in the "middle" of the ordering will increase the power of the test but reduce the degrees of freedom for the test statistic.

Nonparametric statistics

non-parametricnon-parametric statisticsnonparametric
The second test proposed in the paper is a nonparametric one and hence does not rely on the assumption that the errors have a normal distribution.

Resampling (statistics)

resamplingstatistical supportpermutation test
Critical values for this test statistic are constructed by an argument related to permutation tests.

Breusch–Pagan test

Cook–Weisberg testBreusch–Pagan statisticCook-Weisberg test
However some disadvantages arise under certain specifications or in comparison to other diagnostics, namely the Breusch–Pagan test, as the Goldfeld–Quandt test is somewhat of an ad hoc test.

Monotonic function

monotonicitymonotonemonotonic
Also, error variance must be a monotonic function of the specified explanatory variable.

Quadratic function

quadraticquadratic polynomialquadratically
For example, when faced with a quadratic function mapping the explanatory variable to error variance the Goldfeld–Quandt test may improperly accept the null hypothesis of homoskedastic errors.

Robust statistics

robustbreakdown pointrobustness
Unfortunately the Goldfeld–Quandt test is not very robust to specification errors.

Statistical model specification

Model specificationmisspecifiedmisspecification
The Goldfeld–Quandt test detects non-homoskedastic errors but cannot distinguish between heteroskedastic error structure and an underlying specification problem such as an incorrect functional form or an omitted variable.

Ramsey RESET test

RESET test
Jerry Thursby proposed a modification of the Goldfeld–Quandt test using a variation of the Ramsey RESET test in order to provide some measure of robustness.

Glejser test

Herbert Glejser, in his 1969 paper outlining the Glejser test, provides a small sampling experiment to test the power and sensitivity of the Goldfeld–Quandt test.

Monte Carlo method

Monte CarloMonte Carlo simulationMonte Carlo methods
Herbert Glejser, in his 1969 paper outlining the Glejser test, provides a small sampling experiment to test the power and sensitivity of the Goldfeld–Quandt test.

R (programming language)

RR programming languageCRAN
* In R, the "lmtest" package offers the function to perform the Goldfeld–Quandt test.