Causal Analysis for Generalized Interference Problems

Causal inference studies the causal relationships between factors by modeling the underlying data generating process. A common goal in causal inference research is to answer what the effects are of the treatments on the outcomes. Traditional causal inference techniques assume data are independent and identically distributed (IID) and thus ignore interactions among single units. However, a unit’s treatment may affect another unit's outcome (interference), a unit’s treatment may be correlated with another unit’s outcome, or a unit’s treatment and outcome may be spuriously correlated through another unit. Those unit-level interactions are referred to as generalized interference. To capture such nuances, this work proposes a graphical model, "interaction models," which can model the data generating process of data with generalized interference using causal graphs. In this work, I focus on the estimation of causal effects given data with generalized interference, and use interaction models to conduct a systematic analysis of the bias caused by different types of interactions among units. I start with assuming linearity and present the graphical framework, interaction models. The framework applies to a more general setting where interactions can occur between any units. I derive theorems to detect, quantify, and remove the interaction bias. Those results rely on knowing the exact interaction patterns between units. Next, I show how this assumption can be relaxed and present results for when the exact interaction pattern is unknown, where bounding or unbiasedly estimating the causal effects might be possible. I then show how the interaction model framework and the bias analysis results can be generalized for non-parametric models. Finally, I will discuss a special setting where interactions only occur between separated "blocks," so non-IID data can be reduced to block-IID data