Process data from computer-based assessments record the sequence and timing of actions through which respondents solve a task, providing information about both the pace and structure of problem-solving behavior. Modeling such processes across countries is challenging because country-by-response-group cells are often small and unbalanced and the observed transition supports can differ substantially across countries. We propose a hierarchical framework that integrates a Bayesian multi-state survival model with a network-based representation of transition structure. Partial pooling across countries yields country-specific covariate and key-action effects, transition speed, and estimates of between-country heterogeneity. Posterior transition probability networks are embedded in a common latent space using a directed graph auto-encoder adapted to heterogeneous supports, and 1-Wasserstein distances between node-role distributions are evaluated across posterior draws to characterize global network structure while propagating estimation uncertainty. We apply the framework to two problem-solving items from the Programme for the International Assessment of Adult Competencies across 14 countries. The results reveal cross-country heterogeneity in transition speed, systematic response-group differences in global network organization, item-dependent variation in within-group dispersion across countries, and local differences in routing around shared intermediate actions.

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