Max-linear models on directed acyclic graphs

We consider a new structural equation model in which all random variables can be written as a max-linear function of their parents and independent noise variables. For the corresponding graph we assume that it is a directed acyclic graph. We show that the model is max-linear and detail the relation between the weights of the structural equation model and the max-linear coefficients. We characterize all max-linear models which are generated by this structural equation model. This leads to the presentation of a max-linear structural equation model as the solution of a fixed point equation and to a unique minimal DAG describing the relationships between the variables.The model structure introduces an order between the random variables, which yields certain model reductions, represented by subgraphs of the DAG which we call order DAGs. This results also in a reduced form for the regular conditional distributions compared to previous representations.      «

We consider a new structural equation model in which all random variables can be written as a max-linear function of their parents and independent noise variables. For the corresponding graph we assume that it is a directed acyclic graph. We show that the model is max-linear and detail the relation between the weights of the structural equation model and the max-linear coefficients. We characterize all max-linear models which are generated by this structural equation model. This leads to the pre...     »