The Vuong (1989) test compares two models fit to the same observations by
the mean and dispersion of the per-observation log-likelihood differences.
The inflated ordered models reduce to the plain ordered model only in the
limit \(z'\gamma \to \infty\) (every unit in the ordered regime), a point
outside the parameter space, so the likelihood-ratio test has no standard
distribution there and the Vuong test is the comparison used in this
literature (Harris and Zhao 2007; Bagozzi et al. 2015). The raw statistic
and the AIC- and BIC-corrected versions (which penalize the model with more
parameters) are reported, as in pscl::vuong().
Value
An object of class "vuong": a data frame with one row per
correction (raw, AIC, BIC) giving the statistic, the one-sided
p-value that m1 is closer to the truth, the one-sided p-value that m2
is, and the two-sided p-value; positive statistics favor m1.
References
Vuong, Q.H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57, 307-333.
See also
inflation_test(), lr_test(), compare_models()
Other model comparison:
classification(),
compare_models(),
inflation_test(),
lr_test(),
parallel_test(),
split_test()
Examples
set.seed(3)
d <- riop(600, beta = c(0.8, -0.5), tau = c(-0.6, 0.7), gamma = c(0.3, 1), inflate = "bottom")
vuong(iop(y ~ x1 + x2 | z1, d, inflate = "bottom"), oprobit(y ~ x1 + x2, d))
#> Vuong test: m1 = iop(y ~ x1 + x2 | z1, d, inflate = "bottom") [ Inflated ordered probit (inflated category: 0) ]
#> m2 = oprobit(y ~ x1 + x2, d) [ Ordered probit ]
#> positive statistics favor m1
#>
#> correction statistic p_m1_better p_m2_better p_two_sided
#> raw 6.199 0 1 0
#> AIC 6.007 0 1 0
#> BIC 5.583 0 1 0