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Pricing & fairness

GLMs with a small formula language and honest reference levels, frequency–severity summaries, lift and Gini — and then the questions a pricing actuary is increasingly asked to answer: group fairness metrics and a protected-direction audit, ported from the IDE's Hard Data layer.

GLMs

m = sc.glm(df, "claims ~ C(region) + age", "poisson", offset="exposure")
m.relativities()               # exp(β) per level; base level = 1
m.predict(new_business)        # encoded exactly like the training data
m.coef                         # term, estimate, std error, z, p — a Table
sc.rate_table(m)               # the relativities as a wide rating table

m <- sc_glm(df, "claims ~ C(region) + age", "poisson", offset = "exposure")
sc_relativities(m)
sc_predict(m, new_business)    # or predict(m, new_business)
m$coef
sc_rate_table(m)

  factor          level  relativity  estimate
0   line  marine (base)    1.000000  0.000000
1   line    engineering    0.818310 -0.200514
2   line      liability    0.854226 -0.157560
3   line          motor    0.822674 -0.195195
5    age       per unit    0.994120 -0.005897
— Relativities · paid ~ C(line) + age
  basis: base rate exp(intercept) = 35328.4
  · Multiply the base rate by one relativity per factor; the base level of each
    factor is its most frequent level.

The details that matter in practice:

  • Formulas are the useful subset: y ~ a + C(b) + c. C() marks a categorical; text, factor and boolean columns count as categorical without it.
  • Base levels. Scelo's default base is each factor's most frequent level — the natural base for a rating table. base="first" gives the alphabetical convention (R / statsmodels), and base={"region": "GP"} pins it exactly. Fitted values are identical either way; only the parameterisation moves.
  • Families: poisson, gamma, gaussian, binomial, tweedie (power=, needs statmod in R), inverse-Gaussian — default log links except gaussian (identity) and binomial (logit).
  • Engines. Python fits with statsmodels when installed (the IDE's canonical engine) and otherwise with a numpy IRLS tested to agree with statsmodels to 1e-5; R fits with stats::glm.fit. The engine used is printed in the model header.
  • The offset enters as log(offset); rows that cannot enter the fit (missing terms, non-positive offset or gamma response) are dropped and counted.
  • relativities insists on a log link — on any other link, exp(β) is not a relativity, and it says so instead of printing one.

Portfolio summaries

sc.freq_sev(claims, "line")            # exposure, claims, frequency, severity, pure premium
sc.loss_ratio(df, "line")              # loss, premium, loss ratio + total
sc.burning_cost(df, trend=0.05, to_year=2026)
sc.lift(actual, m.fitted, bins=10)     # equal-exposure deciles, A/E per band, Gini
sc.gini(actual, m.fitted)

sc_freq_sev(claims, "line")
sc_loss_ratio(df, "line")
sc_burning_cost(df, trend = 0.05, to_year = 2026)
sc_lift(actual, m$fitted, bins = 10)
sc_gini(actual, m$fitted)

price("claims.csv", "n ~ C(region) + age", severity="amount") / sc_price(...) is the one-liner: a frequency GLM, a Gamma severity GLM on the positive amounts, and one table of frequency × severity = pure premium relativities, with both fitted models in the attributes.

Fairness

sc.fairness(df, "y", "score", "group")          # per-group metrics + the gaps
sc.disparate_impact(df, "score", "group")       # selection rate vs the best-off group
sc.fairness_audit(df, "score", protected="race", legitimate=["age", "vehicle_value"])

sc_fairness(df, "y", "score", "group")
sc_disparate_impact(df, "score", "group")
sc_fairness_audit(df, "score", protected = "race", legitimate = c("age", "vehicle_value"))
  • fairness reports, per group: base rate, selection rate, TPR, FPR, precision, mean score and disparate impact — and its notes state the demographic-parity gap, whether the four-fifths rule passes, and the equal-opportunity and equalised-odds gaps. Scores are thresholded at threshold=0.5; hard 0/1 decisions are recognised and used as they are.
  • fairness_audit asks the sharper question: how much of the prediction's variation beyond the legitimate factors aligns with the protected attribute? It residualises the score on the legitimate factors, measures the protected alignment and disparity of that residual, then shows the same numbers after orthogonalising — with the mitigated score in the attributes, ready to compare.

Function list

design_matrix glm relativities predict rate_table freq_sev loss_ratio burning_cost lift gini price · fairness disparate_impact (parity) fairness_audit — each with the sc_ twin in R.