Path Analysis for Binary Random Variables

The decomposition of the overall effect of a treatment into direct and indirect effects is here investigated with reference to a recursive system of binary random variables. We show how, for the single mediator context, the marginal effect measured on the log odds scale can be written as the sum of the indirect and direct effects plus a residual term that vanishes under some specific conditions. We then extend our definitions to situations involving multiple mediators and address research questions concerning the decomposition of the total effect when some mediators on the pathway from the treatment to the outcome are marginalized over. Connections to the counterfactual definitions of the effects are also made. Data coming from an encouragement design on students’ attitude to visit museums in Florence, Italy, are reanalyzed. The estimates of the defined quantities are reported together with their standard errors to compute p values and form confidence intervals.

Mediation analysis for binary random variables : parametric decomposition of the total effect

This thesis is centered on the evaluation of direct and indirect effects via mediation analysis. A researcher is usually interested in assessing to what extent an exposure variable affects an outcome. However, identifying the overall effect does not answer questions concerning how and why such an effect arises. Single mediation analysis decomposes the overall effect of the exposure on the outcome into an indirect and a direct effect. The former refers to the to the effect of the exposure on the outcome due to a third variable, the mediator, which is supposed to fall in the pathway. The latter effect is the effect of the exposure on the outcome after keeping the mediator to whatever value might be of interest. Specifically, we derived novel exact parametric decompositions of the total effect into direct and indirect effect for binary random variables, both in the counterfactual and path-analysis frameworks. In the single mediation context, we derive parametric expressions of the counterfactual entities and their relationships with the associational definitions coming from the path analysis context. We apply these methodological results on a dataset coming from a randomly allocated microcredit program in Bosnia-Herzegovina to evaluate the effect on client’s bankability. We re-analyse the data, in order to build a mediation scheme that allows a better understanding of the main effect of the study, by assuming business ownership as a possible mediator. We also implement a simulation study to compare the proposed estimator to several competing ones. When multiple mediators are involved, we found alternative definitions for the decomposition of the total effect. These new definitions are more appropriate for variables modelled as a recursive system of univariate logistic regressions. Thus, by making use of graphical models, the overall effect was defined as the sum of the direct, indirect effects and a residual term that is null under certain hypotheses. In general, these expressions are written such that one can maintain the link between effects and their corresponding coefficients in logistic regression models assumed in the system.

Close2U: An App for Monitoring Cancer Patients with a Gamification System to Improve the Engagement

Nowadays, gamification offers several advantages in order to motivate a change in the behavior towards health and wellness. Although it is a relatively new trend, many fields have already realized its potential, and those related to health have also begun to make use of it. This paper introduces an application developed to improve patient monitoring and motivation through the use of gamification. We have applied the mechanics and dynamics of games in a non-game context, such as the introduction of data for health monitoring, in order to attract the patient. With the use of gamification, we make the introduction of data less tedious and, in addition, increase levels of motivation, as a further benefit. In this work we have conducted a user study aimed at evaluating the usability of gamification. We also studied the resources that encourage patients to use the application and how to increase their motivation and satisfaction. The results show that the app is easy to use. Second, they show that we implemented a scalable and self-recursive system. Finally, these results indicate that our system for resources sharing is a system in which patients feel comfortable when sharing and receiving those resources and they encourage us for further developments and studies based on the feedback received.

High-dimensional causal discovery under non-Gaussianity

Summary We consider graphical models based on a recursive system of linear structural equations. This implies that there is an ordering, $\sigma$, of the variables such that each observed variable $Y_v$ is a linear function of a variable-specific error term and the other observed variables $Y_u$ with $\sigma(u) < \sigma (v)$. The causal relationships, i.e., which other variables the linear functions depend on, can be described using a directed graph. It has previously been shown that when the variable-specific error terms are non-Gaussian, the exact causal graph, as opposed to a Markov equivalence class, can be consistently estimated from observational data. We propose an algorithm that yields consistent estimates of the graph also in high-dimensional settings in which the number of variables may grow at a faster rate than the number of observations, but in which the underlying causal structure features suitable sparsity; specifically, the maximum in-degree of the graph is controlled. Our theoretical analysis is couched in the setting of log-concave error distributions.