pscl (version 1.5.9)

vuong: Vuong's non-nested hypothesis test

Description

Compares two models fit to the same data that do not nest via Vuong's non-nested test.

Usage

vuong(m1, m2, digits = getOption("digits"))

Value

nothing returned, prints 3 test statistics and \(p\) values and exits silently.

Arguments

m1

model 1, an object inheriting from class glm, negbin or zeroinfl

m2

model 2, as for model 1

digits

significant digits in printed result

Author

Simon Jackman

Details

The Vuong non-nested test is based on a comparison of the predicted probabilities of two models that do not nest. Examples include comparisons of zero-inflated count models with their non-zero-inflated analogs (e.g., zero-inflated Poisson versus ordinary Poisson, or zero-inflated negative-binomial versus ordinary negative-binomial). A large, positive test statistic provides evidence of the superiority of model 1 over model 2, while a large, negative test statistic is evidence of the superiority of model 2 over model 1. Under the null that the models are indistinguishable, the test statistic is asymptotically distributed standard normal.

Let \(p_i = \hat{Pr}(y_i | M_1)\) be the predicted probabilities from model 1, evaluated conditional on the estimated MLEs. Let \(q_i\) be the corresponding probabilities from model 2. Then the Vuong statistic is \(\sqrt{N} \bar{m}/s_m\) where \(m_i = log(p_i) - log(q_i)\) and \(s_m\) is the sample standard deviation of \(m_i\).

Two finite sample corrections are often considered, based on the Akaike (AIC) and Schwarz (BIC) penalty terms, based on the complexity of the two models. These corrections sometimes generate conflicting conclusions.

The function will fail if the models do not contain identical values in their respective components named y (the value of the response being modeled).

References

Vuong, Q.H. 1989. Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica. 57:307-333.

Examples

if (FALSE) {
data("bioChemists")
## compare Poisson GLM and ZIP
glm1 <- glm(art ~ ., data = bioChemists, family = poisson)
zip <- zeroinfl(art ~ . | ., data = bioChemists, EM = TRUE)
vuong(glm1, zip)


## compare negbin with zero-inflated negbin
nb1 <- MASS::glm.nb(art ~ ., data=bioChemists)
zinb <- zeroinfl(art ~ . | ., data = bioChemists, dist = "negbin", EM = TRUE)
vuong(nb1, zinb)
}