class: center, middle, inverse, title-slide .title[ # Advanced Network Analysis ] .subtitle[ ## Network Analysis and Causal Inference ] .author[ ### Olga Chyzh [www.olgachyzh.com] ] --- ## Reading - Olga V. Chyzh. 2024. How to stop contagion: Applying network science to evaluate the effectiveness of covid-19 vaccine distribution plans. *Journal of Politics* 86 (1): 18-35. - Karthik Rajkumar, Guillaume Saint-Jacques, Iavor Bojinov, Erik Brynjolfsson, and Sinan Aral. A causal test of the strength of weak ties. Science, 377(6612):1304--1310, 202 --- ## Causality and Networks - Suppose I want to know what is the causal effect of a road closure on traffic congestion. Can I simply measure the amount of traffic that passed through the neighboring streets before and after the closure? <img src="./images/Toronto_road_closure.png" alt="" width="1200px" style="display: block; margin: auto;" /> --- ## Causality in Social Networks Now suppose I want to study the effect of smoking on friendships. Suppose "L" took up smoking in period *t*. Can I estimate the effect of this by simply comparing the friendship network between Time 1 to that in Time 2? <img src="16_causal_nets_files/figure-html/unnamed-chunk-3-1.png" alt="" width="500px" style="display: block; margin: auto;" /> --- class: inverse, middle, center # Causality: a refresher --- ## Very Healthy Cereal .pull-left[ <img src="./images/total-cereal.png" alt="" width="1200px" style="display: block; margin: auto;" /> ] .pull-right[ <img src="./images/total-label.png" alt="" width="1200px" style="display: block; margin: auto;" /> ] --- ## Empirical Observation - This cereal sticks to a magnet. <img src="./images/total-magnet.png" alt="" width="500px" style="display: block; margin: auto;" /> --- ## Why Did it Stick? - Propose a theoretical model (that includes a causal mechanism) to explain the observation. -- - Suppose our causal mechanism is that this cereal sticks to a magnet because of its iron content. - A testable hypothesis: cereals that are high in iron stick to a magnet. --- ## Test .pull-left[ <img src="./images/honey-smacks.png" alt="" width="1200px" style="display: block; margin: auto;" /> ] .pull-right[ <img src="./images/honey-smacks-label.png" alt="" width="1200px" style="display: block; margin: auto;" /> ] --- ## Does It Stick? - This cereal does not stick to a magnet. <img src="./images/honey-smacks-magnet.png" alt="" width="350px" style="display: block; margin: auto;" /> --- ## Causal Effect - Unit of analysis: cereal type - Treatment variable (causal variable of interest) `\(T\)`: iron content (high/low) - Treatment group (treated units): Total cereal - Control group (untreated units): Honey Smacks cereal - Outcome variable (response variable) `\(Y\)`: whether it sticks to a magnet (yes/no). --- ## Causality - Counterfactual: Would Total cereal stick to a magnet if it did not have iron? - Two potential outcomes: `\(Y(1)\)` and `\(Y(0)\)` - Causal effect: `\(Y(1)-Y(0)\)` - Fundamental problem of causal inference: only one of the two potential outcomes is observable. - Cannot calculate individual causal effect `\(Y(1)-Y(0)\)`! - Can calculate the average treatment effect by comparing the means of a treatment and a control group. - Importance of control group: must be identical to the treatment group on all factors but the treatment. --- ## The Problem - Causal inference is predicated on comparing the observed to the counterfactual. - Example: To show that the Medici rose to power due to their high network centrality, we must compare the Florentine network to a counter-factual, in which the Medici did not hold a central position. - Often cannot change one aspect of the network while holding all else constant - Cannot change an actor centrality without changing centrality of other actors. - Example 1: Cannot observe what a policy diffusion process across US states would look like in the absence of New York and California. - Example 2: What would the post-World War II international alliance network would look like without the United States? --- ## Two Processes to Consider - Selection - People choose their neighbors. - Influence - Neighbors affect one another. --- ## Influence - When we treat *A*, who receives treatment? <img src="16_causal_nets_files/figure-html/unnamed-chunk-10-1.png" alt="" width="800px" style="display: block; margin: auto;" /> --- ## SUTVA - Classical causal inference assumes one person's treatment does not affect another. - Networks violate this assumption almost by definition. --- class: inverse, middle, center # So how can we study causality in networks? --- ## A Causal Approach - Experiment - Randomly assign features to nodes/edges in networks - Examples: LinkedIn experiment - Natural experiment - Find a sample of social networks, such that some features (e.g.the central nodes' transmission potential) are disabled in some of the networks, but not the others. - Examples: Covid-19 vaccine prioritization policies in the US, censorship on Twitter - Simulations to study different scenarios --- ## Trade-offs | Approach | Strength | Weakness | | ------------------ | ------------------------ | ---------------------- | | Simulation | Complete control | Depends on assumptions | | Natural experiment | Real world | Limited control | | Field experiment | Strongest identification | Expensive | --- class: inverse, middle, center # Simulations: Covid-19 Transmission Under Different Vaccine Priority Scenarios --- ## What groups should be prioritized for vaccines if the goal is to reduce transmission? - oldest? - essential workers? - highest degree? - bridges? --- class: middle, center <img src="images/contagion1.png" alt="" width="600px" style="display: block; margin: auto;" /> --- class: middle, center <img src="images/contagion2.png" alt="" width="600px" style="display: block; margin: auto;" /> --- class: middle, center <img src="images/contagion3.png" alt="" width="700px" style="display: block; margin: auto;" /> --- class: inverse, middle, center # Natural Experiment: Covid-19 Transmission Under Different Vaccine Priority Scenarios --- ## Natural Experiment - Most similar cases: California and Oregon counties - Matching on demographic and economic variables - Treatment: California opened vaccine eligibility to grocery workers (central nodes) about 1 month earlier than Oregon. --- ## Assumptions - Unconfoundedness - SUTVA--stable unit treatment value assumption: treatment assignments for other units do not affect the outcome for unit *i* and that each treatment defines a unique outcome for each unit - Parallel trends --- class: middle, center <img src="images/trends.png" alt="" width="700px" style="display: block; margin: auto;" /> --- class: inverse, middle, center # Field Experiment: LinkedIn --- ## Field Experiment - Randomly vary friend suggestions: weak vs. strong links - Study the effect of the treatment on job applications and new jobs --- ## Field Experiment - Are weak ties or strong ties more valuable? - What do you think of this study? --- ## Things to Consider - Where does the network come from? - Who receives treatment? - Could treatment spill over? - How is identification achieved? - What causal effect is estimated?