Fit a zero-inflated Tweedie regression model

Fits a zero-inflated Tweedie model (via glmmTMB::glmmTMB()) with separate count and zero-inflation components. Returns coefficients on the response scale, randomized quantile residuals, dispersion (phi) and power (p) parameters, and diagnostic plots.

Usage

zeroinflTweedieGLM(formula, data, ziformula = NULL, maxit = NULL, ...)

Arguments

formula

A model formula for the count component (e.g. y ~ x1 + x2). The response must be non-negative.

data

A data frame containing the variables in formula (and ziformula if provided).

ziformula

A one-sided formula for the zero-inflation component (e.g. ~ x1). When NULL (default), the same right-hand side as formula is used for both components. Use ~ 1 for an intercept-only zero-inflation model.

maxit

Optional integer; maximum optimizer iterations passed through as control = glmmTMB::glmmTMBControl(optCtrl = list(iter.max = maxit, eval.max = maxit)). Ignored when the user supplies their own control via ....

...

Additional arguments passed to glmmTMB::glmmTMB().

Value

An object of class c("zeroinflTweedieGLM", "zeroinflGLMfit", "countGLMfit"), a list with:

call

The matched call.

model

The underlying glmmTMB::glmmTMB fit object.

summary

The result of summary() on the fitted model.

phi

The estimated Tweedie dispersion parameter (phi).

p

The estimated Tweedie power parameter (p), in (1, 2). NA if the parameter cannot be extracted from the fit.

coefficients

A list with two data frames, each with columns term, exp.coef, lower.95, upper.95, p.value, and stars:

count

Exponentiated coefficients for the count component.

zero

Exponentiated coefficients for the zero-inflation component (odds ratios for structural-zero membership).

diagnostics

A list with rqr, dispersion_ratio, plot, and r2_plot (see tweedieGLM() for details). No zi_test is included since this model already accounts for zero-inflation.

aic

AIC of the fitted model.

bic

BIC of the fitted model.

Details

Coefficient interpretation:

• Count component: exponentiating a coefficient gives the multiplicative change in the expected Tweedie mean among observations that are not structural zeros, for a one-unit increase in the predictor.

• Zero component: exponentiating a coefficient gives the multiplicative change in the odds of being a structural zero (vs. entering the count process) for a one-unit increase in the predictor. A value greater than 1 means higher odds of a structural zero.

When to use: Zero-inflated Tweedie is the most flexible model in glmOJ. It handles excess zeros and complex variance structures simultaneously. Prefer this over zeroinflPoissonGLM() or zeroinflNegbinGLM() when count data show overdispersion and excess zeros that neither of those families adequately captures. When using countGLM(), this model is fitted only when the DHARMa zero-inflation test flags the base Tweedie fit (p < 0.05).

See also

tweedieGLM(), zeroinflNegbinGLM(), countGLM(), glmmTMB::glmmTMB()

Examples

df <- data.frame(
  y  = c(0, 0, 0, 1.5, 3.2, 0, 0.9, 0, 0, 2.7,
         0, 0, 4.1, 0, 1.2, 0, 0, 5.8, 0, 0),
  x1 = c(1.2, -0.4, 0.8, -1.1, 2.0, 0.3, -0.9, 1.5, -0.2, 0.7,
         -0.5, 0.9, 1.3, -0.3, 0.6, -1.2, 0.1, 2.1, -0.7, 0.4)
)
fit <- suppressWarnings(zeroinflTweedieGLM(y ~ x1, data = df))
print(fit)
#> 
#> Call:
#> zeroinflTweedieGLM(formula = y ~ x1, data = df)
#> 
#> Model family: zeroinflTweedieGLM
#> 
#> Count component (exponentiated coefficients):
#>         term exp.coef lower.95 upper.95 p.value stars
#>  (Intercept)   0.7391   0.1812   3.0144  0.6733      
#>           x1   2.3596   1.1133   5.0011  0.0251     *
#> 
#> Zero-inflation component (exponentiated coefficients):
#>         term exp.coef lower.95 upper.95 p.value stars
#>  (Intercept)   0.5444   0.0309   9.5888  0.6778      
#>           x1   0.9352   0.2112   4.1411  0.9297      
#> 
#> Dispersion (phi): 1.3833
#> Power (p): 1.0360
#> Dispersion ratio: 1.2846
#> AIC: 53.06
plot(fit)


# Intercept-only zero component:
fit2 <- suppressWarnings(
  zeroinflTweedieGLM(y ~ x1, data = df, ziformula = ~ 1)
)