Using Stata's -ml method d2- to estimate a multi-state Markov transition model

I will discuss my experience with Stata's ml method d2 when coding and estimator for a multi-state Markov transition model with unobserved heterogeneity. When analytical derivatives are available, programming a "d2" estimator is in principle straightforward and offers potentially huge rewards in terms of convergence and speed of convergence: When the likelihood is flat, method "d0" may fail to converge (after a many iterations) as numerical derivatives cannot be computed, whereas convergence is often achieved quickly with method "d2". However, when the likelihood function is non-standard, programming a "d2" estimator may be complicated by Stata's limited range of matrix commands. In these cases, the researcher has to be inventive and may have to take a significant "diversion" to compute blocks of the Hessian that should have been straightforward with enhanced matrix capabilities. These "diversions" may be difficult to code and increase evaluation time significantly. With large datasets, this may also push the memory requirements beyond the available limit.