@Model

@Model is the top-level macro that assembles a complete NoLimits model from one or more block macros. It validates the block composition, wires cross-block dependencies, and returns a Model struct ready for data binding and estimation.

Syntax

A minimal model requires only @formulas and at least one parameter (fixed or random):

model = @Model begin
    @fixedEffects begin
        a = RealNumber(0.2)
        sigma = RealNumber(0.3, scale=:log)
    end

    @covariates begin
        t = Covariate()
    end

    @formulas begin
        y ~ Normal(a, sigma)
    end
end

Only macro blocks are allowed inside @Model – no bare Julia statements.

Available Blocks

Each block can appear at most once within @Model:

*At least one of @fixedEffects or @randomEffects must be present.

Validation Rules

@Model enforces the following constraints at construction time:

• @formulas is always required.
• At least one fixed effect or one random effect must be defined.
• @DifferentialEquation requires @initialDE, and vice versa.
• Duplicate blocks are rejected.
• Unknown blocks are rejected.
• Non-macro statements inside @Model are rejected.

When a @DifferentialEquation block is present, additional covariate usage rules are enforced:

• Non-dynamic varying covariates cannot appear in DE expressions.
• Dynamic covariates must be called with a time argument (e.g., w(t)), not used as bare symbols.
• Constant covariates cannot be called as functions in DEs.

Default Behavior for Omitted Blocks

Blocks that are omitted default to empty or inactive states:

• @helpers defaults to an empty NamedTuple.
• @fixedEffects, @covariates, and @randomEffects default to empty blocks.
• @preDifferentialEquation, @DifferentialEquation, and @initialDE default to nothing.

Example: Nonlinear Mixed-Effects Model (No ODE)

using NoLimits
using Distributions

model = @Model begin
    @helpers begin
        sat(u) = u / (1 + abs(u))
    end

    @fixedEffects begin
        a = RealNumber(0.4)
        sigma = RealNumber(0.3, scale=:log)
    end

    @covariates begin
        t = Covariate()
        x = ConstantCovariateVector([:Age, :BMI]; constant_on=:ID)
    end

    @randomEffects begin
        eta = RandomEffect(TDist(6.0); column=:ID)
    end

    @formulas begin
        mu = sat(a + eta^2 + 0.01 * x.Age^2 + log1p(x.BMI^2))
        y ~ Normal(mu, sigma)
    end
end

Example: Full ODE Model

This example demonstrates the full composition of blocks, including a dynamic covariate, a pre-differential-equation transformation, ODE dynamics with a derived signal, and a nonlinear observation model:

using NoLimits
using Distributions

model = @Model begin
    @fixedEffects begin
        a = RealNumber(0.25)
        b = RealNumber(0.1)
        sigma = RealNumber(0.2, scale=:log)
    end

    @covariates begin
        t = Covariate()
        w = DynamicCovariate()
    end

    @randomEffects begin
        eta = RandomEffect(SkewNormal(0.0, 1.0, 0.8); column=:ID)
    end

    @preDifferentialEquation begin
        pre = exp(a + eta^2)
    end

    @DifferentialEquation begin
        s(t) = tanh(w(t) + pre)
        D(x1) ~ -(b + tanh(eta)) * x1 + s(t)^2
    end

    @initialDE begin
        x1 = pre
    end

    @formulas begin
        y ~ Gamma(log1p(abs(x1(t)) + eta^2) + 1e-6, sigma)
    end
end

Model Summary

After construction, use NoLimits.summarize(model) to inspect the declared structure:

model_summary = NoLimits.summarize(model)
model_summary

Runtime Evaluation Helpers

@Model wires internal evaluation functions used during fitting and simulation:

• calculate_prede(...) – evaluate pre-DE expressions
• calculate_initial_state(...) – compute ODE initial conditions
• calculate_formulas_all(...) – evaluate all formula nodes
• calculate_formulas_obs(...) – evaluate observation-node formulas only

When formulas reference ODE states or signals, formula evaluation requires DE solution accessors from get_de_accessors_builder(...).