Boundary-corrected test for zero-inflation (CPB vs ZI-CPB)

A likelihood-ratio test of whether a count needs a structural-zero component. The (untruncated) CPB is nested in the zero-inflated CPB at a structural-zero probability of zero. Because that value lies on the boundary of the parameter space, the LR statistic follows a \(\tfrac12\chi^2_0 + \tfrac12\chi^2_1\) mixture (Self and Liang 1987), which halves the naive \(\chi^2_1\) p-value. The test uses an intercept-only structural-zero probability, so it is a clean single-parameter boundary test. Given two fitted models it refuses the cases where that reference distribution does not hold: a covariate-dependent structural-zero probability (several parameters on their boundary), a fixed-effects zi_cpb() (one count effect per unit, whose number grows with the panel, so the statistic has no fixed-dimension boundary reference), a separated zero equation, models fit to different data, a zero-truncated nest, and CPB models on different supports. It is not a test of a hurdle against a mixture, which are not nested. Compare those with compare_models().

Usage

zi_test(object, object2 = NULL, data = NULL, ...)

Arguments

object: Either a model formula — then data is required and the nested pair is fit internally — or a fitted model (cpb, gec, zi_cpb, or zi_gec).
object2: The second argument: the data frame when object is a formula (so zi_test(y ~ x, mydata) works), or the second fitted model when object is a fit. In the model interface exactly one of the two models must be a zero-inflated zi_cpb (or zi_gec) with intercept-only inflation and the other its untruncated non-inflated nest (cpb, or gec) on the same data.
data: A data frame; an alternative to passing it as object2.
...: Passed to cpb() and zi_cpb() in the formula interface.

Value

An object of class "zi_test" with the two log-likelihoods, the LR statistic, and the boundary-corrected p-value.

Examples

# \donttest{
set.seed(1); x <- rnorm(500)
y <- rzicpb(500, lambda = exp(1.2 + 0.4 * x), alpha = 0.5, pi = 0.3)
zi_test(y ~ x, data = data.frame(y = y, x = x))
#> Boundary-corrected LR test for zero-inflation (CPB vs ZI-CPB)
#>   logLik: CPB = -1099.27, ZI-CPB = -878.83
#>   LR = 440.88,  p = 3.481e-98   (0.5 chi^2_0 + 0.5 chi^2_1 mixture)
#>   Reject: a structural-zero component improves fit.
# }