Fit a Tweedie regression model

Fits a Tweedie GLM (via glmmTMB::glmmTMB()) and returns model coefficients on the response scale (exponentiated), randomized quantile residuals (RQR), estimated dispersion (phi) and power (p) parameters, and diagnostic plots. The Tweedie family generalises Poisson and Gamma distributions and is well-suited to non-negative count data with complex variance structures.

Usage

tweedieGLM(formula, data, assessZeroInflation = TRUE, maxit = NULL, ...)

Arguments

formula

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

data

A data frame containing the variables in formula.

assessZeroInflation

Logical; when TRUE (default), runs a DHARMa simulation-based zero-inflation test after fitting. Issues a warning if significant zero-inflation is detected and adds zi_test to the returned diagnostics. Set to FALSE when calling from countGLM(), which performs its own zero-inflation assessment.

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("tweedieGLM", "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), restricted to (1, 2). Values near 1 resemble Poisson; values near 2 resemble Gamma. NA if the parameter cannot be extracted from the fit.

coefficients

A data frame with columns term, exp.coef, lower.95, upper.95, p.value, and stars (all on the response/exponentiated scale).

diagnostics

A list with:

rqr

Numeric vector of randomized quantile residuals (DHARMa simulation-based, converted to normal scale).

dispersion_ratio

Pearson chi-squared / df.residual.

plot

Patchwork ggplot: fitted vs RQR and histo-QQ.

r2_plot

Squared Pearson residuals vs fitted values.

zi_test

When assessZeroInflation = TRUE, a list with detected (logical), p_value (numeric), and plot (ggplot histogram of DHARMa simulated zero proportions vs observed). NULL when assessZeroInflation = FALSE.

aic

AIC of the fitted model.

bic

BIC of the fitted model.

Details

Three parameters: The Tweedie family is characterised by three estimated quantities: the regression coefficients (mean structure, via a log link), the dispersion phi (Var(Y) = phi * mu^p), and the power p (1 < p < 2). When p is close to 1, the variance structure resembles Poisson; when close to 2, it resembles Gamma.

Coefficient interpretation: Exponentiating a coefficient gives the multiplicative change in the expected response for a one-unit increase in the predictor, holding all other predictors constant.

When to use: Tweedie regression is appropriate for non-negative count data with complex variance structures not well captured by Poisson or negative binomial. If zero-inflation is also present, consider zeroinflTweedieGLM().

See also

zeroinflTweedieGLM(), negbinGLM(), poissonGLM(), countGLM(), glmmTMB::glmmTMB()

Examples

df <- data.frame(
  y  = c(0, 0, 1.5, 3.2, 5.8, 0, 0.9, 4.1, 0, 2.7),
  x1 = c(1.2, -0.4, 0.8, -1.1, 2.0, 0.3, -0.9, 1.5, -0.2, 0.7)
)
fit <- suppressWarnings(tweedieGLM(y ~ x1, data = df))
print(fit)
#> 
#> Call:
#> tweedieGLM(formula = y ~ x1, data = df)
#> 
#> Model family: tweedieGLM
#> 
#> Coefficients (on response scale):
#>         term exp.coef lower.95 upper.95 p.value stars
#>  (Intercept)   1.2700   0.5923   2.7229  0.5391      
#>           x1   1.7403   0.9555   3.1698  0.0701     .
#> 
#> Dispersion (phi): 1.4059
#> Power (p): 1.0420
#> Dispersion ratio: 2.0335
#> AIC: 40.64
plot(fit)