Exploring Nonlinearities in Path Models

In causal analysis, path models are an appropriate tool for studying relationships between social phenomena. However, they assume linear linkages between variables, and hence they are not always suitable for describing the complexity and richness of relationships in social phenomena. In this framework, one of the open problems is to detect the presence of non-linear linkages between variables. This task is usually performed through confirmative tools based on tests of hypotheses, or more rarely on exploratory graphical tools. In our opinion, however, the confirmative and the explorative approaches have to be taken as complementary. In path analysis, the exploratory phase has the main goal of choosing, from all the possible models, a subset of models that are better suited to describing the relationships under study. The confirmative phase then allows the best model in this subset to be chosen. However, whilst many confirmative tools are readily available, graphical tools are rarely used. In this paper, we focus on the detection of interactions between explicative variables in path models, and with this aim we propose an appropriate graphical technique that we call the joint effect plot. The method is based on the analysis of several plots that can be easily drawn and interpreted. Besides the exploratory phase, once a model with interactions has been estimated, the plot also supports qualitative interpretation of the investigated phenomena. The proposed method is applied within a case study. Nonlinearities are explored in a casual model aiming to find the determinants of remittances of a group of Tunisian migrants in Italy.