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; a covariate-dependent structural-zero model is better compared with information criteria and proper scores via compare_dispersion().

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, cpb_fe, or zi_cpb).
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 and the other its non-inflated nest (cpb or cpb_fe); the two may carry any combination of fixed effects and robust/clustered standard errors.
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 = -1089.75, ZI-CPB = -855.76
#>   LR = 467.97,  p = 4.426e-104   (0.5 chi^2_0 + 0.5 chi^2_1 mixture)
#>   Reject: a structural-zero component improves fit.
# }