Rosetta — R ↔ Julia

DRM.jl is the Julia twin of drmTMB, so the modelling grammar is intentionally parallel: the same bf() formula bundle, the same distributional-parameter names, the same structured-effect markers. This page is a side-by-side phrasebook for translating a drmTMB (R) call into DRM.jl (Julia).

Three differences cover almost everything:

	drmTMB (R)	DRM.jl (Julia)
Fit verb	drmTMB(bf(...), family = ...)	drm(bf(...), Family(); data = ...)
Family	lower-case function — gaussian()	capitalised struct — Gaussian()
Scale parameter	sigma	sigma (never tau)

On the R column

The R snippets show drmTMB's grammar (which itself mirrors brms). The family-constructor and S3 method spellings here were reconciled (2026-06-03) against the verified drmTMB NAMESPACE (see docs/dev-log/decisions/2026-06-03-drmtmb-api-snapshot.md); the parameterisations (e.g. Beta φ = 1/σ²) match. drmTMB reuses the base-R stats families (gaussian(), poisson(), Gamma(), binomial()) rather than redefining them. This page is maintained from the Julia side.

The fit call

# R — drmTMB
fit <- drmTMB(bf(y ~ x, sigma ~ x), family = gaussian(), data = dat)

# Julia — DRM.jl
fit = drm(bf(@formula(y ~ x), @formula(sigma ~ x)), Gaussian(); data = dat)

bf() keeps the same shape in both: the first formula's left-hand side is the response and its μ predictor; each later param ~ … formula sets that distributional parameter (sigma defaults to ~ 1).

Families

drmTMB (R)	DRM.jl (Julia)	extra parameters
gaussian()	Gaussian()	sigma
student()	Student()	sigma, nu
skew_normal()	SkewNormal()	sigma, nu (slant alpha; moment form on both sides)
poisson()	Poisson()	— (mean only; zi, hu)
nbinom2()	NegBinomial2()	sigma (dispersion θ = 1/σ²); zi, hu
truncated_nbinom2()	TruncatedNegBinomial2()	sigma (dispersion θ = 1/σ²)
beta()	Beta()	sigma (precision φ = 1/σ²)
beta_binomial()	BetaBinomial()	sigma (φ = 1/σ²)
binomial()	Binomial()	— (mean only)
Gamma()	Gamma()	sigma (CV; shape α = 1/σ²)
lognormal()	LogNormal()	sigma
zero_one_beta()	ZeroOneBeta()	sigma, zoi, coi
tweedie()	Tweedie()	sigma (φ), nu (power p)
cumulative_logit()	CumulativeLogit()	— (ordered cutpoints)
biv_gaussian()	Gaussian() + bf(mu1=…, mu2=…, rho12=…)	sigma1, sigma2, rho12

Formula grammar

Intent	drmTMB (R)	DRM.jl (Julia)
Mean + scale	bf(y ~ x, sigma ~ x)	bf(@formula(y ~ x), @formula(sigma ~ x))
Extra parameter	bf(y ~ x, sigma ~ 1, nu ~ 1)	bf(@formula(y ~ x), @formula(sigma ~ 1), @formula(nu ~ 1))
Random intercept	y ~ x + (1 | g)	@formula(y ~ x + (1 | g))
Random slope	y ~ x + (1 + x | g)	@formula(y ~ x + (1 + x | g))
Crossed REs	y ~ x + (1 | g) + (1 | h)	@formula(y ~ x + (1 | g) + (1 | h))
Two-column response	cbind(s, f) ~ x	@formula(cbind(s, f) ~ x)
Zero-inflation	bf(y ~ x, zi ~ 1)	bf(@formula(y ~ x), @formula(zi ~ 1))
Hurdle	bf(y ~ x, hu ~ 1)	bf(@formula(y ~ x), @formula(hu ~ 1))

Bivariate (two responses + residual correlation)

# R — drmTMB
drmTMB(bf(mu1 = y1 ~ x, mu2 = y2 ~ x, sigma1 = ~ x, sigma2 = ~ 1, rho12 = ~ 1),
       family = biv_gaussian(), data = dat)

# Julia — DRM.jl  (keyword form; ρ12 is the residual correlation, on atanh ρ12)
bf(mu1 = @formula(y1 ~ x), mu2 = @formula(y2 ~ x),
   sigma1 = @formula(sigma1 ~ x), sigma2 = @formula(sigma2 ~ 1),
   rho12 = @formula(rho12 ~ 1))

Structured effects & meta-analysis

Intent	drmTMB (R)	DRM.jl (Julia)
Relatedness matrix	y ~ x + relmat(1 | id), K = K	@formula(y ~ x + relmat(1 | id)), K = K
Animal model	y ~ x + animal(1 | id), A = A	@formula(y ~ x + animal(1 | id)), A = A
Phylogenetic	y ~ x + phylo(1 | species), tree = tree	@formula(y ~ x + phylo(1 | species)), tree = tree
Spatial	y ~ x + spatial(1 | site), coords = xy	@formula(y ~ x + spatial(1 | site)), coords = xy
Meta-analysis (univariate)	gaussian() + meta_V(v)	Gaussian() + meta_V(v)
Meta-analysis (bivariate, known sampling covariance)	meta_V(V = meta_vcov_bivariate(...)) inside mu1	meta_vcov_bivariate(...) passed as drm(...; V = V) — see meta-analysis

Post-fit accessors

drmTMB (R)	DRM.jl (Julia)
coef(fit) / fixef(fit)	coef(fit) / fixef(fit)
vcov(fit)	vcov(fit)
confint(fit, method = "wald")	confint(fit; method = :wald)
confint(fit, method = "profile") / profile(fit)	confint(fit; method = :profile)
parametric bootstrap CIs	bootstrap_ci(bf(...), Family(); data, B = 300)
logLik(fit)	loglik(fit)
AIC(fit) / BIC(fit)	aic(fit) / bic(fit)
nobs(fit)	nobs(fit)
deviance(fit)	deviance(fit)
df.residual(fit)	dof_residual(fit)
ranef(fit)	ranef(fit)
random-effect SDs	re_sd(fit) / vc(fit)
sigma(fit)	sigma(fit)
rho12(fit)	planned (parity gap)
corpairs(fit)	corpairs(fit) / corpairs_data(fit)
fitted(fit) / residuals(fit)	fitted(fit) / residuals(fit)
predict(fit, newdata) (response mean)	predict(fit, newdata; type = :response)
predict every distributional parameter at new data	predict_parameters(fit, newdata; type = :response)
in-sample fitted per-observation parameters	marginal_parameters(fit)
build a covariate grid for prediction	prediction_grid(reference; predictor = values, …)
simulate(fit)	simulate(fit)
summary(fit)	show(fit) / coeftable(fit) (no summary method)
weights(fit)	planned (parity gap)
family(fit)	family(fit)
is_converged(fit) / convergence diagnostics	is_converged(fit) / check_drm(fit)

Prediction

drmTMB centres prediction on predict(fit, newdata), which returns the response-scale mean. DRM.jl matches that and adds first-class verbs for the other distributional parameters:

Intent	drmTMB (R)	DRM.jl (Julia)
Response-scale mean at new data	predict(fit, newdata)	predict(fit, newdata; type = :response)
Linear-predictor (link) scale	predict(fit, newdata, type = "link")	predict(fit, newdata; type = :link)
Predict all distributional parameters	(capability: predict each bf() parameter)	predict_parameters(fit, newdata; type = :response)
In-sample fitted per-obs parameters	(capability: per-observation fitted parameters)	marginal_parameters(fit)
Build a covariate grid	(capability: hold-others / sweep grid)	prediction_grid(reference; predictor = values, …)

• predict(fit, newdata; type = :response) returns the response-scale mean (the family inverse link applied to Xβ̂ — exp/logistic/identity); type = :link returns Xβ̂. Univariate gives a vector; bivariate gives Dict(:mu1 => …, :mu2 => …).

• predict_parameters(fit, newdata) returns a Dict(:mu => …, :sigma => …, …) with one entry per distributional parameter the family carries (plus any of :nu, :zi, :hu, :zoi, :coi); a bivariate fit returns :mu1, :mu2, :sigma1, :sigma2, :rho12. type = :response (default) applies each parameter's inverse link (σ via exp, ρ12 via tanh); type = :link returns each working-scale linear predictor.

• marginal_parameters(fit) reads the stored in-sample fitted parameters straight from the fit (no recomputation); in-sample it equals predict_parameters(fit, data) on the response scale.

• prediction_grid(reference; predictor = values, …) builds a newdata column table by sweeping the named predictors over their value ranges (their Cartesian product) while holding every other predictor at its reference (mean for numeric columns). It is pure data, so it composes directly: predict_parameters(fit, prediction_grid(...)).

drmTMB's exact R spelling for per-parameter prediction is not asserted here (only the capability is); the response-mean predict row is the verified parity point.

Naming rules to remember

• Scale is sigma, never tau. bf(y ~ x, tau ~ x) is rejected — use sigma. (Group-level phylo/spatial/study variances are reported as named covariance summaries, not as a residual scale.)

• rho12 is the bivariate residual correlation between the two responses (on the atanh scale). It is only valid in the keyword bf(mu1 = …, mu2 = …, rho12 = …) form — not as a univariate parameter.

• ML is the default. REML is an option (the likelihoods are not comparable across different fixed-effect structures, so ML is used for model selection).

See also the R ↔ Julia bridge for the planned drmTMB(..., engine = "julia") round-trip via JuliaCall.