Fit a Poisson regression model

Fits a Poisson GLM and returns model coefficients on the response scale (exponentiated), randomized quantile residuals (RQR), a Pearson dispersion ratio, and a two-panel diagnostic plot.

Usage

poissonGLM(formula, data, ...)

Arguments

formula

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

data

A data frame containing the variables in formula.

...

Additional arguments passed to stats::glm().

Value

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

call

The matched call.

model

The underlying stats::glm fit object.

coefficients

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

diagnostics

A list with:

rqr

Numeric vector of randomized quantile residuals.

dispersion_ratio

Pearson chi-squared / df.residual. Values substantially above 1 (rule of thumb: > 1.5) suggest overdispersion; consider negbinGLM().

plot

A patchwork ggplot: fitted values vs RQR (left) and normal Q-Q of RQR (right).

aic

AIC of the fitted model.

Details

Coefficient interpretation: Poisson regression models the log of the expected count. Exponentiating a coefficient gives the multiplicative change in the expected count for a one-unit increase in the predictor, adjusting for simultaneous linear changes in other predictors. For example, 1.5 means a 50% higher expected count.

Condition checking: Inspect diagnostics$dispersion_ratio. A value near 1 is consistent with the Poisson assumption (mean = variance). The RQR diagnostic plot should show points scattered randomly around zero with approximately normal QQ behaviour.

See also

negbinGLM(), zeroinflPoissonGLM(), countGLM(), stats::glm()

Examples

df <- data.frame(
  y  = c(0L, 1L, 2L, 3L, 5L, 0L, 2L, 4L, 1L, 3L),
  x1 = c(1.2, -0.4, 0.8, -1.1, 2.0, 0.3, -0.9, 1.5, -0.2, 0.7)
)
fit <- poissonGLM(y ~ x1, data = df)
print(fit)
#> 
#> Call:
#> poissonGLM(formula = y ~ x1, data = df)
#> 
#> Model family: poissonGLM 
#> 
#> Coefficients (on response scale):
#>         term exp.coef lower.95 upper.95
#>  (Intercept)   1.7989   1.0683   3.0290
#>           x1   1.3396   0.8572   2.0936
#> 
#> Dispersion ratio: 1.1658
#> AIC: 39.02
plot(fit)