Abstract
In this paper, an extension of linear Markovian structural causal models is introduced,called distributed-lag linear structural equation models (DLSEMs),where each factor of the joint probability distribution is adistributed-lag linear regression with constrained lag shapes.DLSEMs account for temporal delays in the dependence relationshipsamong the variables and allow to assess dynamic causal effects.As such, they represent a suitable methodology to investigate the effectof an external impulse on a multidimensional system through time.In this paper, we present the dlsem package for Rimplementing inference functionalities for DLSEMs.The use of the package is illustrated through an example on simulated dataand a real-world application aiming at assessing the impact of agriculturalresearch expenditure on multiple dimensions in Europe.
Highlights
Structural causal models (SCMs, Pearl 2000, Chapter 5) represent one of the prevalent methodologies for causal inference in contemporary applied sciences
A Markovian SCM is such that a directed acyclic graph (DAG) encodes causal relationships among the variables, which implies a factorization of the joint probability distribution according to conditional independence relationships
In a linear parametric formulation, each factor of the joint probability distribution is a linear regression model, and a causal effect is associated to each edge, directed path or couple of nodes in the DAG to represent average changes in the value of a variable induced by an intervention provoking a unit variation in the value of another variable
Summary
Structural causal models (SCMs, Pearl 2000, Chapter 5) represent one of the prevalent methodologies for causal inference in contemporary applied sciences. In a linear parametric formulation (linear Markovian SCM), each factor of the joint probability distribution is a linear regression model, and a causal effect is associated to each edge, directed path or couple of nodes in the DAG to represent average changes in the value of a variable induced by an intervention provoking a unit variation in the value of another variable. We introduce an extension of linear Markovian SCMs, called distributed-lag linear structural equation models (DLSEMs), where each factor of the joint probability distribution is a distributed-lag linear regression with constrained lag shapes. They were introduced for the first time by Magrini (2018) in the context of lag exposure assessment.
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