Model equations
yit = β₀ + f(t) + βᵀxit + b₀i + b₁it + uregion(i) + εit
Mixed longitudinal submodel (morphology) — x includes environmental and socioeconomic covariates Julia · planned
λrs(t | xi(t), bi) = λrs,0(t) · exp{ βrsᵀ xi(t) + γrsᵀ bi }, P(Δt) = exp(Q Δt)
Continuous-time multistate, interval censoring (E0→E4) Julia · planned
hit = P(Ti ∈ (t, t+1] | Ti > t, Hit); g(hit) = α + βᵀ xi, g ∈ {logit, cloglog}
Discrete-time hazard, quarterly, E1→E3 implemented
Si(t) = ∏k ≤ t (1 − hik), F(t) = 1 − Ei[Si(t)]
Cumulative incidence for E3 implemented
AIC = 2k − 2 ln L, BIC = k ln n − 2 ln L, VIFj = 1 / (1 − R²j), Σ = V Λ Vᵀ (PCA)
Selection and multivariate diagnostics implemented
Fit result
Select the variables and click “Fit”.
Mixed model — REML / BLUP
log Ti = Xβ + Zu + ε, u ~ N(0, σ²uI), ε ~ N(0, σ²eI), V = σ²e(I + λZZᵀ), λ = σ²u/σ²e
β̂ = (XᵀV⁻¹X)⁻¹XᵀV⁻¹y; λ maximizes the REML likelihood
û = λ Zᵀ V⁻¹ (y − Xβ̂), ICC = σ²u / (σ²u + σ²e)
BLUP: group effect shrunk toward 0 (stronger for smaller n)
Click “Fit REML / BLUP”.
FAMD + clustering
Click “Run FAMD”.
FAMD in 3 dimensions (by cluster)
Hazard surface