friendship networks results

I was able to reproduce segregation patterns that look like the actual data.  Then, I ran multiple runs to see how the percent same-color friends changed depending on the share of same-color in the school. The line is flatter than in the actual data, so my next step is to vary the other parameters and see if I can reproduce those plots.


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I am modeling how social interactions could affect secondary students’ likelihood to attend higher education, in particular throughout variables such as knowledge of the higher education system, willingness to go to higher education-engagement, and academic knowledge.

In the model I’m firstly working with the knowledge of the higher education system and how this knowledge it is transferred between students. I’m also adding the role of parents and teachers (not yet done) in this process.

The outcomes I’m looking in the model are the distribution of knowledge of the higher education system, those who are able to trespass a threshold, and the rate of the knowledge of the 10% of the students with highest knowledge and the 10% of students with lowest knowledge.

I assumed the transference as a weighted average (still to check) of the personal knowledge and other agents’ knowledge. I realized this process depend a lot of the initial distribution of knowledge and the initial distribution of friendship.

In the model I included possibilities to change:

–          Number of students

–          Initial distribution of knowledge

–          Number of friends (N-links)

–          Stratification, which I understand as the possibility to make friends with other students with similar/different amounts of knowledge in HE.

–          A rate of transference of the knowledge

–          The possibility to do just random interactions

–          The action of parents as an accelerator or barrier to the knowledge transference

I’m still trying to define the optimal number of ticks. If I let the model run I end up in most of the cases with an average distribution of knowledge. Interestingly some particular configurations could lead to a polarization of the knowledge that is an increase of the stratification. It seems important here to understand better the final rate of transference of knowledge and how this rate could be increased.

I think this model could be useful to better understand possible policies.








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Final Model: Teacher-Child Interactions

In my final model, I added two classroom activities: free play (children move about randomly) and small group activity (clusters of 4 children). I also added two types of intervention: reducing conflict by 1) sending children to time-out; 2) increasing teacher warmth. When a teacher has a conflict with a child, she now becomes red and waits for 3 ticks, to try to simulate more of her time being spent on children with high levels of externalizing behavior (and therefore less time with the other children in the classroom).

I plotted overall classroom level of conflict. When I observe the dynamic effect of the two types of interventions, time-out appears to have a stronger effect of reducing conflict in the classroom. In the screenshot of my model, a child in time-out is depicted in green.

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Voters’ choice of targeted, universal or no provision of early childhood education

In this model, voters choose between targeted, universal and no provision of ECE. Their choice depends on whether they have young children, their income, the share of the population that is eligible for targeted ECE, whether they have close ties to other citizens, their ties’ income and whether their ties have young children. Individuals have an initial endowment of children but can have more children as years go by (at different rates, depending on whether they are white or minority). All children eventually grow up and are no longer considered as young children for the purpose of voting. The model is for only one generation.

The next three steps are: (1) to incorporate more generations, so that once children grow up and become citizens they also vote for targeted, universal or no ECE provision; (2) to make the model more complex, to include not only citizens but also teacher unions’ and elected officials’ preferences; and (3) to explore my second question of interest, concerning what per-child level of funding is awarded to ECE once society has elected to provide either targeted or universal ECE.

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Final – State-Level School Choice Policy Adoption

Policy adoption occurs if a majority of state school board members vote yes on the policy (a new policy is proposed at each tick).  School board members are located in congressional districts (patches); and, their votes are a function of their constituency members’ propensities to vote yes for the policy (weighted; weights are adjustable via a slider).  There are seven member types (e.g., teachers unions), and their initial propensities are adjustable via sliders (members propensities change slightly over time randomly).  The model contains an on-off switch that allows a board member’s vote to be contingent on the votes of the board members in the surrounding four districts.  Based on theoretically plausible assumptions (e.g., initial propensity endowments), the passage of school choice policies oscillates significantly over time – this is in line with my expectations.  Next steps include making constituent members’ propensities over time dependent on — to varying degrees — the propensities of other members’ propensities within their district, as well as on the propensities of like members across districts.

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Model of College Choice

I ended up trying to model college choice. Students will attend college if two conditions are met:

  1. Their ability is greater than the college selectivity.
  2. The adjusted cost (college tuition minus the student’s predicted income gain from college) is less than the student’s income.

Students who don’t satisfy these conditions for any college will not attend college. Students who satisfy these conditions for multiple colleges will attend the one that maximizes their utility — highest selectivity, lowest adjusted cost.

Students then move toward their desired college (if applicable). Colleges with larger students are those that are the most desirable. There are also switches that show each college’s characteristics.

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final child care selection model

Here’s the child care selection process in action! Family budgets and costs of care are now on sliders; the choice algorithm can maximize quality (default) or minimize distance to the centers (on the switch); and we can define school-readiness only as a value-add from centers, or allow 10% of kids to be school-ready from the get-go (on the second switch). Finally, the monitors show enrollment and school-readiness rates, allowing us to watch how quality changes based on budget-constraints and the nature of family choice. In the future, I plan to make trade-offs between quality and convenience more nuanced, create ties between families to share information, and make information about center quality imperfect. For now, this has been a great introduction to agent-based modeling and its application to our research interests. Thanks to the instructors and TAs!

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Day 3: “Math belongingness” & gendered pathways into different Math levels

“Math belongingness” and gendered pathways into Math levels

This is an attempt to model how male/female students enter different level math classes in junior high school through high school (when math tracking often begins).

The starting point is that the gender achievement gap in math (test scores) have nearly dimished in the US, but attitudes towards math (self-concept, affinity) are still starkly gendered.  This model is an attempt to capture the differences in levels of performance and students’ sense of ‘belongingness’ to math measured by various aspects of schooling: (for now)– students increase/decreases in their level of math ‘belonging’ based on whether the teacher is the same gender as the student, whether the student has friends of the same gender who perform well, and the students’ own math performance. 

Currently, the model runs so that over time, all students end up in the higher level math classes.  This may be a manifestation of my overly simple model at this point, and/or the fact the mechanisms currently driving the patterns are such that the characteristics leading to increases in levels of belongingness outweight the characteristics leading students to decrease in their level so belongingness. 

Next steps need to be to give students different teachers each year, give more complex mechanisms that change students’ performance levels and sense of belongingness to math.

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Philanthropy to Schools and the Colbert Bump

Model of Colbert Bump

Social ties, including viewership of the Colbert Report, help more projects get funded

This model shows how Stephen Colbert (the big guy in the middle) can boost donations to teachers via merely by mentioning the organization on his show. allows teachers across America to describe projects they would like funded for their classrooms.  Donors log on and select which project they want to give to, at what rate.

The Colbert Nation (Colbert’s viewers) are shown as red, white, or blue people, linked to him by viewership arrows.   As they choose whether and how much to donate, they consider how connected they and their friends are to Stephen Colbert, how recently they’ve heard Stephen pitch it, how often they have given before, whether a few key friends have donated, and how geographically close they are to the closest project a teacher has listed for funding.

Teachers currently seeking donations are shown with briefcases.  Teachers whose projects have already been fully funded turn into smiling faces like described (credit mukith).  The graph shows that the most gifts, and the most conversions into fully funded projects, occur in the days immediately following a mention on “The Colbert Report.”  The rate of decay of these mentions is one of the variables we wish to explore through this model.

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Jon’s model of charter school applicants

I’m looking at how the demographics of high-performing urban charter schools might change as the schools improve their performance and increase their visibility.  Here, my families use only three criteria for school selection: distance from home; school quality; and school SES profile.  I’ll explain.

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