View source: R/fitdiagnostics.R
lr.test | R Documentation |
Conduct the likelihood-ratio test for two nested extreme value distribution models.
lr.test(x, y, alpha = 0.05, df = 1, ...)
x , y |
Each can be either an object of class “fevd” (provided the fit method is MLE or GMLE) or a single numeric giving the negative log-likelihod value for each model. |
alpha |
single numeric between 0 and 1 giving the significance level for the test. |
df |
single numeric giving the degrees of freedom. If both |
... |
Not used. |
When it is desired to incorporate covariates into an extreme value analysis, one method is to incorporate them into the parameters of the extreme value distributions themselves in a regression-like manner (cf. Coles, 2001 ch 6; Reiss and Thomas, 2007 ch 15). In order to justify whether or not inclusion of the covariates into the model is significant or not is to apply the likelihood-ratio test (of course, the test is more general than that, cf. Coles (2001) p 35).
The test is only valid for comparing nested models. That is, the parameters of one model must be a subset of the parameters of the second model.
Suppose the base model, m0, is nested within the model m1. Let x
be the negative log-likelihood for m0 and y
for m1. Then the likelihood-ratio statistic (or deviance statistic) is given by (Coles, 2001, p 35; Reiss and Thomas, 2007, p 118):
D = -2*(y
- x
).
Letting c.alpha be the (1 - alpha) quantile of the chi-square distribution with degrees of freedom equal to the difference in the number of model parameters, the null hypothesis that D = 0 is rejected if D > c.alpha (i.e., in favor of model m1).
A list object of class “htest” is returned with components:
statistic |
The test statistic value (referred to as D above). |
parameter |
numeric vector giving the chi-square critical value (c.alpha described above), the significance leve (alpha) and the degrees of freedom. |
alternative |
character string stating “greater” indicating that the alternative decision is determined if the statistic is greater than c.alpha. |
p.value |
numeric giving the p-value for the test. If the p-value is smaller than alpha, then the decision is to reject the null hypothesis in favor of the model with more parameters. |
method |
character string saying “Likelihood-ratio Test”. |
data.name |
character vector of length two giving the names of the datasets used for the test (if “fevd” objects are passed) or the negative log-likelihood values if numbers are passed, or the names of x and y. Although the names may differ, the models should have been fit to the same data set. |
Eric Gilleland
Coles, S. (2001) An introduction to statistical modeling of extreme values, London, U.K.: Springer-Verlag, 208 pp.
Reiss, R.-D. and Thomas, M. (2007) Statistical Analysis of Extreme Values: with applications to insurance, finance, hydrology and other fields. Birkhauser, 530pp., 3rd edition.
fevd
, taildep.test
data(PORTw)
fit0 <- fevd(PORTw$TMX1, type="Gumbel")
fit1 <- fevd(PORTw$TMX1)
fit2 <- fevd(TMX1, PORTw, scale.fun=~STDTMAX)
lr.test(fit0, fit1)
lr.test(fit1, fit2)
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