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glmOJ

glmOJ is an R package that provides a structured workflow for count regression modeling. It wraps glm, MASS::glm.nb, and pscl::zeroinfl to fit, diagnose, and interpret count regression models, with all output reported on the response scale rather than the link scale.

What the package does

Count data — non-negative integers like the number of events, species, or visits — require specialized regression models. glmOJ guides the analyst through four steps:

  1. Summarize the response variable and its relationship to predictors before modeling.
  2. Fit one or more count regression models from the supported families.
  3. Assess model conditions using randomized quantile residuals (RQR) and the Pearson dispersion ratio.
  4. Interpret all output on the response scale (exponentiated coefficients with confidence intervals).

Supported model families

Family Function Use when
Poisson poissonGLM() Counts with mean ≈ variance
Negative binomial negbinGLM() Counts with variance > mean (overdispersion)
Zero-inflated Poisson zeroinflPoissonGLM() Excess zeros + equidispersed non-zero counts
Zero-inflated negative binomial zeroinflNegbinGLM() Excess zeros + overdispersed non-zero counts

The general-purpose countGLM() fits all four families and selects the best by AIC, annotated with dispersion and zero-inflation diagnostics.

Package functions

Data summarization

  • summarizeCountData(formula, data) — Produces numerical summaries (mean, variance, variance-to-mean ratio, zero count) and a plot of the count response against predictors. The plot type adapts to the number and type of predictors (histogram, scatter, violin, heatmap, etc.).

Model fitting

Each individual fitter returns exponentiated coefficients with 95% Wald confidence intervals, randomized quantile residuals, a Pearson dispersion ratio, and a two-panel diagnostic plot (fitted values vs. RQR | normal Q-Q of RQR).

  • poissonGLM(formula, data) — Poisson regression via stats::glm.
  • negbinGLM(formula, data) — Negative binomial regression via MASS::glm.nb.
  • zeroinflPoissonGLM(formula, data, ziformula) — Zero-inflated Poisson via pscl::zeroinfl. Separate coefficient tables for the count and zero-inflation components.
  • zeroinflNegbinGLM(formula, data, ziformula) — Zero-inflated negative binomial via pscl::zeroinfl.

Model selection

  • countGLM(formula, data, ziformula) — Fits all four families, selects the best by AIC, and returns a plain-language recommendation informed by the Pearson dispersion ratio and observed vs. expected zero counts.

Condition checking

All model fitters compute:

  • Randomized quantile residuals (RQR) — For a well-fitting model, RQRs should be approximately standard normal. The diagnostic plot shows them against fitted values (checking for structure) and on a normal Q-Q plot.
  • Pearson dispersion ratio — Pearson chi-squared divided by residual degrees of freedom. Values near 1 are consistent with the assumed model; values substantially above 1 (rule of thumb: > 1.5 from a Poisson fit) suggest overdispersion and motivate switching to negative binomial.

Coefficient interpretation

All coefficients are reported on the response scale (exponentiated). For the count component of any model, 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, a value of 1.5 means a 50% higher expected count.

For the zero-inflation component of ZI models, the exponentiated coefficient gives the multiplicative change in the odds of being a structural zero.

Installation 

# Install from GitHub
# install.packages("pak")
pak::pak("ojaroker/glmOJ")