Migration Guide

This guide helps users transition from statsmodels (Python) and R packages (mgcv, lme4) to Aurora-GLM.

From statsmodels

API comparison:

Task	statsmodels	Aurora-GLM
Gaussian GLM	sm.OLS(y, X).fit()	fit_glm(X, y, family="gaussian")
Logistic regression	sm.Logit(y, X).fit()	fit_glm(X, y, family="binomial", link="logit")
Poisson regression	sm.Poisson(y, X).fit()	fit_glm(X, y, family="poisson")
Gamma GLM	sm.GLM(y, X, family=sm.families.Gamma()).fit()	fit_glm(X, y, family="gamma")
Standard errors	result.bse	result.std_errors_
P-values	result.pvalues	result.p_values_
Predict	result.predict(X_new)	result.predict(X_new)
AIC	result.aic	result.aic_

Key differences:

• Aurora-GLM uses fit_glm() for all families; statsmodels has separate classes (sm.OLS, sm.Logit, etc.)

• Aurora result attributes use trailing underscores (aic_ vs aic)

• Aurora uses family= and link= string shortcuts; statsmodels requires importing family objects

# statsmodels
import statsmodels.api as sm
model = sm.GLM(y, sm.add_constant(X), family=sm.families.Gamma(sm.families.links.log()))
result_sm = model.fit()

# Aurora-GLM
from aurora.models.glm import fit_glm
result = fit_glm(X, y, family="gamma", link="log")

From R mgcv

GAM comparison:

Task	R mgcv	Aurora-GLM
Single smooth	gam(y ~ s(x), data=df)	fit_gam(x, y, n_basis=10)
Multiple smooths	gam(y ~ s(x1) + s(x2), data=df)	fit_gam_formula("y ~ s(x1) + s(x2)", data)
Mixed terms	gam(y ~ s(x1) + x2, data=df)	fit_gam_formula("y ~ s(x1) + x2", data)
REML selection	gam(..., method="REML")	fit_additive_gam(..., method="REML")
Basis dimension	s(x, k=10)	s(x, k=10) (identical syntax)
Plot smooth	plot(model)	plot_smooth(result)

# R mgcv
library(mgcv)
m <- gam(y ~ s(x1, k=10) + s(x2) + x3, data = df, method = "REML")
summary(m)

# Aurora-GLM
from aurora.models.gam import fit_gam_formula
result = fit_gam_formula("y ~ s(x1, k=10) + s(x2) + x3", df, method="REML")
print(result.summary())

From R lme4

GAMM / mixed model comparison:

Task	R lme4	Aurora-GLM
Random intercept	lmer(y ~ x + (1|subject))	fit_gamm("y ~ x + (1 | subject)", data)
Random slope	lmer(y ~ x + (x|subject))	fit_gamm("y ~ x + (x | subject)", data)
Intercept + slope	lmer(y ~ x + (1+x|subject))	fit_gamm("y ~ x + (1 + x | subject)", data)
Nested effects	lmer(y ~ x + (1|a/b))	fit_gamm("y ~ x + (1 | a/b)", data)
Crossed effects	lmer(y ~ x + (1|a) + (1|b))	fit_gamm("y ~ x + (1 | a) + (1 | b)", data)
Variance	VarCorr(m)	result.variance_components
Fixed effects	fixef(m)	result.beta_parametric
Predict	predict(m, newdata)	predict_from_gamm(result, X_new)

# R lme4
library(lme4)
m <- lmer(y ~ x + (1 + time | subject), data = df, REML = TRUE)
summary(m)

# Aurora-GLM
from aurora.models.gamm import fit_gamm
result = fit_gamm(
    formula="y ~ x + (1 + time | subject)",
    data=df,
    covariance="unstructured",
)
print(result.summary())

Numerical validation

Aurora-GLM is validated against R and statsmodels to within 1e-6 tolerance:

• GLM coefficients match statsmodels and R’s glm()

• GAM smooth terms match R’s mgcv::gam()

• GAMM variance components match R’s lme4::lmer()

• The 3,377 tests in the test suite verify this agreement

If results differ between Aurora and R, check:

1. Convergence tolerance (try decreasing tol)

2. Number of IRLS iterations (increase max_iter)

3. Basis dimension (try increasing n_basis or k=)

4. Smoothing parameter (compare lambda_ vs R’s sp)