Skill: Generalized Linear Model

Use When

• User has count data (e.g., read counts, event counts) requiring Poisson or negative binomial regression
• User has a proportion or binary outcome requiring binomial regression
• User wants a unified framework for regression across different data distributions
• Use cases: RNA-seq count modeling, species abundance counts, clinical event rates

Inputs

• Required:
  • Data table (CSV or TSV) with a response variable and one or more predictor columns
  • Response variable name
  • Predictor variable name(s)
  • GLM family: poisson, binomial, or gaussian
• Optional:
  • Link function: default per family (log for Poisson, logit for Binomial, identity for Gaussian)
  • Offset variable name (for Poisson rate models, e.g., log library size)
  • Check overdispersion: true (default for Poisson)
  • Output directory (default: ./glm_output)

Workflow

1. Read data; validate that response variable is compatible with the specified family (non-negative integers for Poisson, 0/1 or proportions for Binomial).
2. Fit GLM using the specified family and link function.
3. If Poisson: test for overdispersion (dispersion statistic). If overdispersed, automatically refit with quasi-Poisson or negative binomial and report.
4. Report for each coefficient: estimate (on link scale), standard error, z-statistic, p-value, exponentiated estimate (rate ratio for log link, odds ratio for logit link) with 95% CI.
5. Report model fit: null deviance, residual deviance, AIC, degrees of freedom.
6. Generate diagnostic plots: residuals vs. fitted (Pearson residuals), Q-Q plot of deviance residuals.
7. Write results table (TSV), model summary (text), and diagnostic plots (PDF) to output directory.
8. Report overdispersion finding and family choice justification.
9. Save the executable analysis script (analysis_code.py or analysis_code.R) and software version manifest (session_info.txt) used to produce results.

Output Contract

• Coefficient table (TSV): term, estimate, std_error, z_statistic, p_value, exp_estimate, ci_lower, ci_upper
• Model fit summary (TSV): family, link, null_deviance, residual_deviance, aic, df_residual
• Diagnostic plots (PDF)
• Overdispersion test result (Poisson only, printed to stdout)
• Reproducibility artifacts: analysis_code.py or analysis_code.R, plus session_info.txt

Limits

• Negative binomial GLM is preferred over Poisson when count data is overdispersed (common in RNA-seq — use DESeq2 instead for that use case).
• Binomial GLM requires the response to be a proportion [0,1] or a two-column success/failure matrix for aggregated data.
• Does not handle zero-inflated data; use hurdle or zero-inflated models separately.
• Common failure: passing a continuous response with Poisson family — verify data type before running.