On aggregation invariance of multinomial processing tree models

Multinomial processing tree (MPT) models are prominent and frequently used tools to model and measure cognitive processes underlying responses in many experimental paradigms. Although MPT models typically refer to cognitive processes within single individuals, they have often been applied to group data aggregated across individuals. We investigate the conditions under which MPT analyses of aggregate data make sense. After introducing the notions of structural and empirical aggregation invariance of MPT models, we show that any MPT model that holds at the level of single individuals must also hold at the aggregate level when it is both structurally and empirically aggregation invariant. Moreover, group-level parameters of aggregation-invariant MPT models are equivalent to the expected values (i.e., means) of the corresponding individual parameters. To investigate the robustness of MPT results for aggregate data when one or both invariance conditions are violated, we additionally performed a series of simulation studies, systematically manipulating (1) the sample sizes in different trees of the model, (2) model parameterization, (3) means and variances of crucial model parameters, and (4) their correlations with other parameters of the respective MPT model. Overall, our results show that MPT parameter estimates based on aggregate data are trustworthy under rather general conditions, provided that a few preconditions are met.