magnus919_agent-skills/actuarial-risk-modeling/references/model-families.md

Model Families

Choose a family from the outcome support and data-generating structure, not from the algorithm currently in fashion. A candidate is not validated merely because it converges.

Structure	Candidate families	Questions and checks
Continuous, approximately symmetric	Linear regression, transformed regression, robust regression	Linearity, variance, leverage, residual dependence, transformation interpretation
Binary or categorical	Logistic/probit, multinomial/ordinal models	Class prevalence, separation, link fit, calibration, threshold costs
Counts	Poisson, negative binomial, quasi-likelihood, hurdle/zero-inflated models	Exposure offset, overdispersion, structural zeros, integer support, dependence
Positive skewed amounts	Gamma/log-link, lognormal, inverse Gaussian, robust or quantile models	Positive support, retransformation, tail fit, heteroscedasticity, aggregate implications
Zero plus positive amount	Two-part/hurdle, frequency-severity, Tobit only when censoring assumptions fit	Zero mechanism, conditional severity, exposure, dependence between parts
Proportion or bounded outcome	Binomial/beta-type models, fractional response	Denominator, boundary masses, dependence, calibration
Event time	Survival, accelerated-failure-time, proportional-hazards, recurrent-event models	Censoring, truncation, competing risks, time-varying covariates, proportionality
Repeated or clustered	Fixed/random effects, mixed models, GEE, hierarchical models	Cluster definition, within-cluster correlation, missingness, transportability
Ordered time	Dynamic regression, ARIMA/state-space, exponential smoothing, volatility models	Information cutoff, stationarity, seasonality, interventions, rolling validation
Extreme or tail-focused	Quantile, generalized Pareto/extreme-value, tail-adjusted GLM, scenario analysis	Threshold choice, tail dependence, sparse data, extrapolation uncertainty

Generalized linear model checklist

Specify the response distribution, link, linear predictor, exposure offset, estimation method, and interpretation scale. Check whether the variance function matches the data, whether the link is plausible, whether overdispersion or zero inflation remains, and whether residuals are independent enough for the intended inference. For an insurance rate, distinguish a frequency offset from a severity weight. A convenient transformation is not an offset.

Common traps

• Poisson does not become appropriate merely because the target is called a “count.”
• Negative binomial handles overdispersion, not arbitrary dependence or zero mechanisms.
• A log-transformed response is not automatically equivalent to a log-link model for the original conditional mean; retransformation and target interpretation matter.
• Tobit is a censored-outcome model, not a generic answer for any target with zeros.
• A random effect is not a magic correction for omitted-variable bias or leakage.
• A survival model needs an event origin and censoring story, not only a duration column.
• Extreme-value extrapolation is fragile when the tail threshold or data-generating regime is uncertain. Show sensitivity rather than one authoritative tail number.

Model comparison

Compare candidates on a predeclared, decision-relevant evaluation design. Include a simple baseline and a transparent benchmark. Compare both performance and failure behavior: calibration, tail loss, segment stability, operational cost, interpretability, data needs, and monitoring burden. Complexity must earn its place with evidence.