Struct LinearMixedModel 

pub struct LinearMixedModel { /* private fields */ }

A fitted random-intercept linear mixed model

yᵢⱼ = xᵢⱼᵀβ + bⱼ + εᵢⱼ, bⱼ ~ N(0, σ²_b), εᵢⱼ ~ N(0, σ²_e),

for observations i nested in groups j (one random intercept per group). The marginal covariance is V = σ²_e I + σ²_b ZZᵀ; because there is a single grouping factor, V⁻¹ is block-diagonal in closed form, so the whole fit reduces to a one-dimensional search over the variance ratio λ = σ²_b/σ²_e, profiling out β (by GLS) and σ²_e analytically at each λ. Method::Reml (default) gives unbiased variance components.

The headline diagnostics are the variance components, the intraclass correlation ICC = σ²_b/(σ²_b + σ²_e) (the share of variance between groups, and the correlation of two observations in the same group), and the BLUPs — shrinkage-predicted group intercepts.

Implementations

impl LinearMixedModel

pub fn new(x: Array2<f64>, y: Array1<f64>, groups: &[usize]) -> Result<Self>

Fit a random-intercept model of y on fixed-effect design X with group labels groups (one per observation; arbitrary integer labels are remapped internally), by REML.

X carries the fixed effects including any intercept column, as elsewhere in the crate.

Errors

• RegressionError::EmptyInput / RegressionError::ShapeMismatch.
• RegressionError::NoResidualDegreesOfFreedom if n ≤ p.
• RegressionError::InvalidResponse if there are fewer than two groups.
• RegressionError::RankDeficient if the GLS information is singular.

pub fn with_method( x: Array2<f64>, y: Array1<f64>, groups: &[usize], method: Method, ) -> Result<Self>

Like LinearMixedModel::new with an explicit Method.

pub fn n_observations(&self) -> usize

Number of observations.

pub fn n_parameters(&self) -> usize

Number of fixed-effect coefficients.

pub fn n_groups(&self) -> usize

Number of groups (levels of the random intercept).

pub fn method(&self) -> Method

Estimation method used.

pub fn coefficients(&self) -> ArrayView1<'_, f64>

Fixed-effect coefficients β̂ (GLS at the estimated variance ratio).

pub fn covariance(&self) -> ArrayView2<'_, f64>

Fixed-effect covariance σ̂²_e (XᵀV⁻¹X)⁻¹.

pub fn coefficient_standard_errors(&self) -> Array1<f64>

Fixed-effect standard errors.

pub fn residual_variance(&self) -> f64

Residual (within-group) variance σ̂²_e.

pub fn group_variance(&self) -> f64

Between-group (random-intercept) variance σ̂²_b.

pub fn variance_ratio(&self) -> f64

Estimated variance ratio λ̂ = σ̂²_b / σ̂²_e.

pub fn icc(&self) -> f64

Intraclass correlation ICC = σ̂²_b / (σ̂²_b + σ̂²_e) — the fraction of total variance attributable to between-group differences, equivalently the correlation between two observations in the same group.

pub fn random_effects(&self) -> ArrayView1<'_, f64>

BLUPs — best linear unbiased predictors of the group random intercepts b̂_j, indexed by densified group order (first-seen order of the labels). Each is the group’s mean residual shrunk toward zero by (λ n_j)/(1 + λ n_j).

pub fn log_likelihood(&self) -> f64

The profile log-likelihood (REML or ML per method) at the estimated variance components.

pub fn aic(&self) -> f64

AIC. Under ML the parameter count is p + 2 (fixed effects plus the two variance components); under REML, where fixed effects are integrated out, only the two variance components are counted.

Trait Implementations

impl Clone for LinearMixedModel

fn clone(&self) -> LinearMixedModel

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for LinearMixedModel

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.