Fit and compare count regression models

Fits all four count regression models supported by glmOJ (Poisson, negative binomial, zero-inflated Poisson, zero-inflated negative binomial), selects the best by AIC, and provides a plain-language recommendation informed by dispersion and zero-inflation diagnostics.

Usage

countGLM(formula, data, ziformula = NULL, ...)

Arguments

formula: A model formula for the count component (e.g. y ~ x1 + x2). The response must be a non-negative integer count variable.
data: A data frame containing the variables in formula (and ziformula if provided).
ziformula: A one-sided formula for the zero-inflation component passed to zeroinflPoissonGLM() and zeroinflNegbinGLM(). When NULL (default), the same right-hand side as formula is used.
...: Additional arguments passed to each individual model fitter.

Value

An object of class "countGLM", a list with:

call: The matched call.
fits: A named list of successfully fitted model objects (poisson, negbin, zeroinfl_poisson, zeroinfl_negbin). Any model that failed to converge is omitted.
aic_table: A named numeric vector of AICs, sorted ascending.
best_model: Character name of the model with the lowest AIC.
recommendation: A plain-language character string explaining the selection, including dispersion and zero-inflation context.

Details

Model selection: AIC is the primary criterion. Lower AIC indicates a better balance of fit and parsimony.

Heuristic diagnostics (computed from the Poisson fit and used to annotate the recommendation, not to override AIC):

Overdispersion: Pearson dispersion ratio > 1.5 from the Poisson fit suggests the negative binomial family may be more appropriate.
Zero-inflation: If the observed number of zeros exceeds 1.3x the number of zeros expected under a Poisson model, excess zeros are flagged.

Individual models can be accessed via result$fits$negbin, etc., and support print(), summary(), and plot().

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)
)
result <- countGLM(y ~ x1, data = df)
#> Warning: iteration limit reached
#> Warning: iteration limit reached
print(result)
#> 
#> Call:
#> countGLM(formula = y ~ x1, data = df)
#> 
#> AIC comparison:
#>             model   AIC
#>           poisson 39.02
#>            negbin 41.02
#>  zeroinfl_poisson 41.43
#>   zeroinfl_negbin 43.43
#> 
#> Selected model: poisson
#> 
#> Recommendation:
#>   Poisson was selected by AIC (AIC = 39.02). The Poisson dispersion
#>   ratio is 1.17, consistent with equidispersion. There are 1.4x more
#>   zeros than expected under Poisson (observed: 2, expected: 1.4),
#>   suggesting zero-inflation.
#> 
summary(result)
#> Summary of selected model (poisson):
#> 
#> 
#> Call:
#> poissonGLM(formula = formula, data = data)
#> 
#> 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