Web-based Supporting Materials for Fitting and Interpreting Continuous-Time Latent Markov Models for Panel Data

The CTMC log-likelihood component is in the curved exponential family, with natural parameters log(λij) and ∑ i 6=j λij corresponding to sufficient statistics nT (i, j) and dT (i). Individual level baseline covariates wh are added via log(λij) = β T ijw h, where h denotes the individual and wh and βij are p-dimensional vectors corresponding to p covariates. For convenience, we list the intensity parameters {log(λij) : i, j ∈ S; i 6= j} as a q-dimensional vector ψ, indexing each i, j pair in ψ by u. This allows us to derive the score and information for all intensity parameters simultaneously, which is particularly useful if one assumes the same covariate effect for more than one transition intensity. Using the notation i[u] and j[u] to yield the i and j corresponding to u, the uth entry of the vector score function for ψ is l̇(ψ)[u] = nT (i[u], j[u])− dT (i[u]) exp (ψ[u]) . The Hessian matrix for ψ is diagonal with non-zero entries