Weighting strategies for modelling life course history events via pairwise composite marginal likelihood

Models using large temporal datasets often feature complex likelihood functions. In the context of life course history data, the dimension of integration may increase with the number of time periods considered which rules out Maximum Simulated Likelihood (MSL) estimation techniques. An alternative is to use the Composite Marginal Likelihood (CML) inference approach, which replaces high-dimensional integrals by a compounding of bivariate probabilities. The current paper delves into the issue of how to form CML functions. CML is a flexible tool which allows to use different weights on different bivariate margins (typically 0 or 1) which will affect goodness-of-fit, efficiency as well as computation speed. The typical approach consists of using the pairing combinations of temporally close choice situations and assign a weight of 0 to the other pairs. Other weighting strategies such as using nonrectangular or random weights are possible but rarely used In this paper, we propose a large simulation exercise based on a real dataset on car availability over the life course in Germany to compare the finite-sample performances of the CML approach under alternative weighting strategies. Our results indicate that the typical weighting approach is outperformed in a large majority of cases. We also find that introducing observed and random heterogeneity in weights improves model performances in terms of parameter recovery. Finally, we unravel the important role played by spurious state dependence in car availability across the life course.