Clustering Random Curves Under Spatial Interdependence with Application to Service Accessibility ( Supplementary Material )

1 Supplemental Material 1: Fitting Algorithm The estimation algorithm for the general model is a two-step (EM) iterative procedure to find the maximum of the likelihood of the observed data. The estimation algorithm iteratively computes (E-step) and maximizes (M-step) the expected likelihood of the complete data conditional on the observed data. The joint log-likelihood is l(α,β, σ ε , σ 2 s , θ) = log f(Y |γ,Z;α,β, σ ε ) + log f(γ; σ s) + log f(Z; θ) ≈ log f(Y |γ,Z;α,β, σ ε ) + log f(γ;σ s) + n ∑